problem solving for place value

Crore

Lakhs

Thousands

Ones

Ten-Crore

(TC)

10,00,00,000

Crore

(C)

1,00,00,000

Ten-Lakhs

(TL)

10,00,000

Lakhs

(L)

1,00,000

Ten Thousands

(TTh)

10,000

Thousands

(Th)

1000

Hundreds

(H)

100

Tens

(T)

10

Ones

(O)

1

Millions

Thousands

Ones

Hundred-millions

(HM)

100,000,000

Ten-millions

(TM)

10,000,000

Millions

(M)

1,000,000

Hundred-Thousands

(HTTh)

100,000

Ten-Thousands

(TTh)

10,000

Thousands

(Th)

1000

Hundreds

(H)

100

Tens

(T)

10

Ones

(O)

1

2500

Hundreds

500

5069

Thousands

5000

7235

Ones

5

9050

Tens

50

29975

ten thousands

20,000

tens

70

8627

Tens

20

Ones

7

208764

Lakhs/Hundred-thousands

2,00,000 or

200,000

Hundreds

700

720000

Ten thousands

20,000

Lakhs/Hundred-thousands

7,00,000 or

700,000

8

?

4

?

8

0

4

6

2

8

4

5

7

8

9

1

2

5

9

7

2

1

3

7

0

9

1

2

0

9

8

6

In a number, of a digit is the value of the position of that digit within the given number. For example, the place value of the digit 5 in 19530 is 500.

The of any digit in the number is the value of the digit itself. For example, the face value of 5 in 19530 is 5.

The following place value chart is used represent decimal numbers:

Question 11: Write the following numbers in the place value charts:

(ii) 325.006

(iii) 0.976

Question 12: Fill in the blanks:

(i) 1 × 100 + 2 × 10 + 8 × 1 + 5 × 1/10 + 2 × 1/100 = _____.

(ii) 2 × 1000 + 28 × 10 + 1 × 1/10 + 1 × 1/100 = ________.

(iii) 0.008 + 1.07 + 0.5 = _______.

(iv) 300 + 4 + 45 + 0.0006 + 0.007 + 0.08 = ______.

(i) 1 × 100 + 2 × 10 + 8 × 1 + 5 × 1/10 + 2 × 1/100 = 128.52

(ii) 2 × 1000 + 28 × 10 + 1 × 1/10 + 1 × 1/100 = 2280.11

(iii) 0.008 + 1.07 + 0.5 = 1.578

(iv) 300 + 4 + 45 + 0.0006 + 0.007 + 0.08 = 349.0876

Practice Questions:

1. Find the place value of 6 for the following numbers:

(iii) 497612

2. The digits in the tens and the thousands place of a number are 3 and 9, respectively. The digit in the ones and the ten thousands places are 3 and 4 more than the digit in tens place. If the digit in the hundreds place is three less than the digit in ten thousands place, find the number.

3. Fill in the blanks:

(i) 3000 + 700 + _____ + 8 = 3758.

(ii) 200 + 9050 + 4 = ______.

(iii) 2000 + 0.009 + 12.23 + 300 = _____.

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Place Value – Definition with Examples

Updated on January 10, 2024

Place Value is an essential and fundamental concept in mathematics that enables us to comprehend and work effectively with numbers. At Brighterly , we understand the importance of mastering place value for building a strong foundation in mathematics, as it plays a critical role in arithmetic operations, problem-solving, and overall number sense. In this comprehensive article, we will delve deep into place value, unraveling its various aspects and significance.

What is Place Value?

Place value is the system of attributing a value to a digit in a number depending on its position. It is a crucial concept that facilitates our ability to read, write, and comprehend numbers, making calculations more straightforward and efficient. Place value ensures that each digit in a number contributes differently based on its position. For instance, consider the number 7,548. The place value of 7 is 7,000, as it is in the thousands place; the place value of 5 is 500, as it is in the hundreds place; the place value of 4 is 40, as it is in the tens place; and finally, the place value of 8 is 8, as it is in the ones place.

Understanding place value is the cornerstone of the base-10 numeral system, which is the most commonly used number system worldwide. By learning place value, children develop a strong foundation in mathematics, enabling them to tackle more complex topics with ease. At Brighterly, we focus on teaching place value concepts in a fun and engaging manner, ensuring that children develop a clear understanding and appreciation of the importance of place value in their mathematical journey.

Place Value Worksheet PDF

Place Value Worksheet

Place Value Worksheets Free PDF

Place Value Worksheets Free

Don’t forget to use math worksheets for kids available on the Brighterly to further enhance your skills!

Place Value Chart

A place value chart is a visual representation of the positions of digits in a number. It helps us understand the value of each digit and makes it easy to compare and manipulate numbers. A typical place value chart consists of columns for units, tens, hundreds, thousands, and so on.

Place Value Meaning

The meaning of place value is the value assigned to each digit based on its position within a number. As we move from right to left, each position represents a power of 10. For example, in the number 7,651, the place value of 7 is 7,000 (7 * 10^3), the place value of 6 is 600 (6 * 10^2), the place value of 5 is 50 (5 * 10^1), and the place value of 1 is 1 (1 * 10^0). This system is essential for understanding how numbers work and for performing calculations.

Comparison Between Indian and International System

The Indian and International systems of place value differ in the way they group digits. In the Indian system, digits are grouped in pairs after the hundredth place, whereas in the International system, digits are grouped in threes. For example, the number 5,678,901 is written as 56,78,901 in the Indian system and as 5,678,901 in the International system. This difference affects the naming of larger numbers and the way they are read aloud. You can learn more about the Indian and International systems of place value by visiting this link.

Place Value for Decimals

Place value for decimals works similarly to whole numbers but extends to the right of the decimal point. Each position to the right of the decimal point represents a negative power of 10. For example, in the number 0.123, the place value of 1 is 1/10 (1 * 10^(-1)), the place value of 2 is 2/100 (2 * 10^(-2)), and the place value of 3 is 3/1000 (3 * 10^(-3)). Understanding place value for decimals is crucial for working with fractions, measurements, and other real-world quantities.

Place Value in Numbers

Place value in numbers is the cornerstone of the base-10 numeral system, which is the most commonly used number system worldwide. Understanding place value in numbers allows us to represent and manipulate numbers efficiently. For example, when we add or subtract numbers, we align them according to their place values and perform operations on corresponding digits.

Face Value in Maths

Face value is the value of a digit itself, irrespective of its position in a number. In other words, the face value of a digit is the same no matter where it appears in a number. For example, the face value of 5 in the numbers 5, 25, 354, and 5,807 is always 5.

Difference Between Place Value and Face Value

The main difference between place value and face value is that place value depends on the position of a digit within a number, while face value is the value of a digit itself, independent of its position. Place value helps us understand the overall value of a number and perform arithmetic operations, while face value is a more basic concept that shows the value of individual digits.

Solved Examples on Place Value

To better understand place value, let’s look at some solved examples:

Find the place value of 7 in the number 4,783.

In this number, 7 is in the hundreds place. So, the place value of 7 is 7 * 10^2 = 700.

Determine the place value of 2 in the number 0.023.

In this number, 2 is in the hundredths place. So, the place value of 2 is 2 * 10^(-2) = 2/100 = 0.02.

Free Printable Place Value Worksheets

Place Value Worksheets With Answers

Practice Problems on Place Value

Try solving these practice problems to test your understanding of place value:

• Find the place value of 3 in the number 3,762.
• Determine the place value of 4 in the number 0.049.
• Calculate the place value of 6 in the number 16,205.

Place value is an indispensable concept in mathematics that forms the foundation for understanding and working with numbers effectively. By mastering the intricacies of place value, students can perform arithmetic operations more efficiently, read and write numbers accurately, and develop a robust sense of number sense. At Brighterly, we emphasize the importance of place value in our curriculum, ensuring that children build a strong mathematical foundation from the very beginning.

Through our innovative teaching methods, interactive activities, and engaging content, Brighterly strives to make learning place value an enjoyable and memorable experience for our young learners. We believe that by fostering a deeper understanding of place value, we are empowering students to conquer more complex mathematical concepts with ease and confidence.

As students progress through their mathematical journey, the significance of place value becomes increasingly apparent. From basic arithmetic operations to advanced problem-solving, place value remains a vital tool that bolsters mathematical comprehension and critical thinking. It is our mission at Brighterly to equip children with the knowledge and skills necessary to navigate the fascinating world of mathematics, starting with the mastery of place value.

Frequently Asked Questions on Place Value

What is the place value of 0 in a number.

The place value of 0 in a number is always 0, no matter its position. Zero serves as a placeholder, indicating that there are no units, tens, hundreds, etc., in that position.

Why is place value important?

Place value is important because it allows us to represent and manipulate numbers efficiently. It also forms the basis for arithmetic operations, problem-solving, and overall number sense.

How is place value used in everyday life?

Place value is used in everyday life when we read and write numbers, count, measure, and perform calculations. It helps us understand the value of digits in different positions and makes it easier to perform operations like addition, subtraction, multiplication, and division.

How can I teach place value to children?

Teaching place value to children can be done through various methods, such as using base-10 blocks, place value charts, manipulatives, and real-life examples. Engaging activities and games can also help children develop a strong understanding of place value concepts.

What is the difference between place value and expanded form?

Place value refers to the value of a digit based on its position in a number, while expanded form is a way of writing a number by breaking it down into its individual place values. For example, in the number 543, the place value of 5 is 500, the place value of 4 is 40, and the place value of 3 is 3. The expanded form of this number is 500 + 40 + 3.

• Place Value Concepts – National Council of Teachers of Mathematics
• Place Value – BBC Bitesize
• Understanding Place Value – National Center on Improving Mathematics Instruction

As a seasoned educator with a Bachelor’s in Secondary Education and over three years of experience, I specialize in making mathematics accessible to students of all backgrounds through Brighterly. My expertise extends beyond teaching; I blog about innovative educational strategies and have a keen interest in child psychology and curriculum development. My approach is shaped by a belief in practical, real-life application of math, making learning both impactful and enjoyable.

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Place value

Here you will learn about place value , including the names and values of the different positions.

Students will first learn about place value as part of their work with numbers and operations in base ten in elementary school.

What is place value?

Place value is the value of each digit within a number.

A number is made up of digits. For example, the number 54 has two digits, 5 and 4. The value of each digit can help us understand the size of the number.

To determine the value of a digit within a number you use a place value chart.

For example, for 54, the 5 is in the tens column and the 4 is in the ones column.

This means that the number 54 is equivalent to 5 tens and 4 ones.

5 tens is the same as 5\times{10}=50 and 4 ones is the same as 4\times{1}=4.

Adding 50+4 gives us the number 54.

Whole number place value

Here are the digits to the left of the decimal point.

Let’s write the number nine million, four hundred and fifty thousand, three hundred and eighty two in the place value chart:

Notice you use a comma after the millions digit (9) and the thousands digit (0).

The comma is used to the left of the decimal point to separate 3 digits at a time.

If the value within a column is 0, you must write a zero for that place value. Here, if you missed the 0 in the thousands position, the number would read 945,382 which is a different number from the number above.

The place value chart above shows positions up to the millions. However, you can use place value to represent very large numbers.

Decimal place value

Here are the digits to the right of the decimal point .

Let’s write the number two and thirty four thousandths in the place value chart:

There is a period after the ones digit (2). The period tells us that the next part of the number is a decimal or less than 1.

If the value within a column is 0, you must write a zero for that place value. Here, if you missed the 0 in the tenths position, the number would read 2.34 which is a different number from the number above.

The place value chart above shows numbers down to the thousandths. However, you can use place value to represent very small numbers.

Common Core State Standards

How does this relate to 2nd grade math, 4th grade math and 5th grade math?

• Grade 2 – Numbers and Operations in Base 10 (2.NBT.A.3) Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.
• Grade 4 – Numbers and Operations in Base 10 (4.NBT.A.2) Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form.
• Grade 5 – Numbers and Operations in Base 10 (5.NBT.A.3) Read, write, and compare decimals to thousandths.

How to write the value of a digit in a number

In order to write the value of a digit in a number:

Find the digit within the number.

Use the place value chart to find the position.

Write the value of the digit.

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Place value examples

Example 1: whole number place value.

What is the value of the digit 3 in 4,163?

• Find the digit within the number.  

2 Use the place value chart to find the position.

The 3 is in the ones column.

3 Write the value of the digit.

The value of the digit 3 in the number 4,163 is 3 ones, or 3.

Example 2: whole number place value

What is the value of the digit 4 in 385,431?

The 4 is in the hundreds column.

The value of the digit 4 in the number 385,431 is four hundreds, or 400.

Example 3: whole number place value

What is the value of the digit 2 in 1,025,634?

The 2 is in the ten thousands column.

The value of the digit 2 in the number 1,025,634 is twenty thousands, or 20,000.

Example 4: decimal place value

What is the value of the digit 2 in 3.264?

The 2 is in the tenths column.

The value of the digit 2 in the number 3.264 is two tenths, or 0.2.

Example 5: decimal place value

What is the value of the digit 7 in 0.078?

Recall the place value of that column.

The 7 is in the hundredths column.

The value of the digit 7 in the number 0.078 is seven hundredths, or 0.07.

Example 6: decimal place value

What is the value of the digit 4 in 10.054?

Locate the digit within the number.

The 4 is in the thousandths column.

The value of the digit 4 in the number 10.054 is four thousandths, or 0.004.

Teaching tips for place value

• When teaching place value, base ten blocks and other manipulatives can be used to help students visualize place value and see how each position relates to the others.
• Place value is based on patterns in our number system, which many students will pick up on. Asking questions like “What do you notice about these numbers?” or “How does the value of a number change if you change the place value of the digits?” can encourage students to think more broadly about the underlying structure of our place value system.
• Regularly exposing students to place value ideas helps them develop a deeper understanding of our number system. Instead of just using worksheets, incorporate it into math each day with a place value game. Something as simple as “I am thinking of a number that has more than 4 hundreds, what could it be?” can help students remember and think flexibly about place value.
• Reinforce the connection between standard form, expanded form and word form by asking students to provide all three for any given number.

Easy mistakes to make

• Including too many digits All of the digits after a place value position are sometimes wrongly included. For example, What is the value of 4 in the number 243? \quad 43 {\color{red}✘} \quad 40 {\color{green}✔}
• Including a oneths column The first column to the right of the decimal point is the tenths column – there is no oneths column. For example, What is the value of the digit 2 in the number 3.524? \hspace{0.5cm} Two tenths or 0.02 {\color{red}✘} \hspace{3cm} Two hundredths, or 0.02 {\color{green}✔} (Thinking that the first decimal \hspace{1.7cm} (The first decimal position is tenths position is oneths and the second \hspace{1.7cm} and the second is hundredths) is tenths)

Related rounding numbers lessons

• Rounding numbers
• Rounding decimals
• Significant figures

Practice place value questions

1. What is the value of 2 in 475,321?

Two hundreds

The digit 2 is in the tens column, so the value is 2 tens or 20.

2. What is the value of 1 in 1,000,253?

One hundred thousand

The digit 1 is in the millions column, so the value is 1 million or 1,000,000.

3. What is the value of 3 in 483,201?

Ten thousand

The digit 3 is in the thousands column, so the value is 3 thousands or 3,000.

4. What is the value of 7 in 6.072?

Seven hundreds

Seven tenths

Seven hundredths

The digit 7 is in the hundredths column, so the value is 7 hundredths or 0.07.

5. What is the value of 8 in 0.008?

Eight thousandths

Eight tenths

Eight thousands

The digit 8 is in the thousandths column, so the value is 8 thousandths or 0.008.

6. What is the value of 4 in 4.825?

Four thousandths

The digit 4 is in the ones column, so the value is 4 ones or 4.

Place value FAQ

Our number system is called Base Ten, because ten is the value used to create the place value groupings. That is why all of the place value positions (like the tens place or hundreds place) are multiples of 10. This is also why younger students practice skip counting by tens, which ultimately helps them recognize patterns in our number system.

Place value helps you understand the size of a number and gives meaning to the digits in each position. An understanding of place value can help you when comparing numbers and ordering numbers and is also essential when operating with numbers.

Per the Common Core, in fifth grade students work with the tenths place, the hundredths place and the thousandths place. Sixth graders should extend this to smaller positions. It is also important to be mindful of standard expectations, as they may vary from state to state.

The next lessons are

• Factors and multiples
• Fractions operations

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Place Value Word Problems

Read the Whole Word Problem: Firstly, read the entire word problem so you can understand it somewhat better. Then, ask yourself questions each time you’re confronted by a word problem. After that, check the work whenever you’re done.

A step-by-step guide to solving place value word problems

Here’s a step-by-step guide to solving place value word problems:

• Read the problem carefully and identify the given information: In a place value word problem, you are usually given a number or a set of numbers, along with some specific information about the digits or their positions. Read the problem carefully identify the given information, and make sure you understand what the problem is asking you to find.
• Identify the place value of the digits: The place value of a digit determines the value of the digit based on its position in the number. Identify the place value of the digits that are given or asked for in the problem. For example, if the problem involves finding the value of the hundreds place or the thousands place, make sure you know what these places are and how to calculate their values.
• Write the number in expanded form: Expanded form is a way of writing a number as the sum of its digits multiplied by its place values. Write the number in expanded form to help you visualize the value of each digit in the number.
• Perform the necessary operations: Once you have identified the given information and the place values of the digits, perform the necessary operations to solve the problem. This may involve adding, subtracting, multiplying, or dividing the digits to find the answer.
• Check your answer: After you have completed the problem, double-check your work to make sure your answer makes sense and is consistent with the problem. You can also verify your answer by using estimation or by working the problem backward.

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By following these steps, you should be able to solve place value word problems with greater ease and accuracy.

The problem asks for a number that has 6 thousands, a number of hundreds that is 2 less than the number of thousands, a number of tens that is 1 more than the number of hundreds, and a number of ones that is 3 more than the number of thousands. What is this number?

Solution: You want to find the number 6 … … …

 2 fewer than a thousand is 4. 1 more tens than hundreds is 5. 3 more ones than thousands is 9.

So, it’s 6459.

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Mastering grade 5 math the ultimate step by step guide to acing 5th grade math, mastering grade 3 math the ultimate step by step guide to acing 3rd grade math, mastering grade 5 math word problems the ultimate guide to tackling 5th grade math word problems, mastering grade 2 math word problems the ultimate guide to tackling 2nd grade math word problems, mastering grade 4 math word problems the ultimate guide to tackling 4th grade math word problems.

by: Effortless Math Team about 2 years ago (category: Articles )

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Place Value

September 3, 2022.

Scheme of work: Key Stage 3: Year 7: Term 1: Place Value

Prerequisite Knowledge

• Find 1000 more or less than a given number.
• Recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• Order and compare numbers beyond 1000
• Identify, represent and estimate numbers using different representations
• Round any number to the nearest 10, 100 or 1000
• Solve number and practical problems involving the above and increasingly large positive numbers.
• Read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include zero and place value.

Key Concepts

• The ability to arrange digits in a place value table is crucial to accessing future topics such as fractions, percentages and many more.
• When multiplying and dividing by 10, 100 and 1000, students can benefit from visualising the digit shift between columns in the place value table.
• To interpret a number scale, students need to have a secure understanding of using the place value table.
• Students often confuse the direction of the inequality symbols when comparing numbers.

Working Mathematically

• Consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals.
• Reason mathematically
• Extend their understanding of the number system; make connections between number relationships,
• Solve problems
• Select appropriate concepts, methods and techniques to apply to unfamiliar and non-routine problems.

Subject Content

• understand and use place value for decimals, measures and integers of any size
• order positive and negative integers, decimals and fractions; use the number line as a model for ordering the real numbers; use the symbols =, > and <
• use the four operations, including formal written methods, to integers and decimals.

Place Value Resources

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Extended Learning

Problem Solving

Mr Mathematics Blog

Increasing and decreasing functions.

How to identify increasing and decreasing functions using differentiation.

Includes common student mistakes and video tutorial.

Proving Sums of Series Using Mathematical Induction

A-Level Further Mathematics Blog: How to set up a proof by induction using the sums of series.

Maximise Effective Questioning in Mathematics

Explore how Mr-Mathematics.com resources enhance effective questioning, engage students, and connect math to real-life problems.

Problem solving with place value

I can use my knowledge of place value to solve problems

Lesson details

Key learning points.

• Measures are not always presented in the same format.
• Sometimes a measure must be converted into a desired format.
• Real-life context can be useful in determining the most useful unit of measurement.

Common misconception

You have to convert to the same unit to decide if a measure is the same as another.

For metric units it is possible to compare the digits. Any conversion within metric has the same digits in the same order.

Metric - Metric units are based around the standard units of metre, gram and litre.

Prefix - A prefix is a group of letters attached to the front of a root (word) to make a new word, for example tricycle.

Centi - Centi placed before a unit means (1/100)

Milli - Milli placed before a unit means (1/1000)

Kilo - Kilo placed before a unit means 1000 times.

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Place Value Worksheets

And base 10 blocks.

Our place value worksheets focus on deepening a student's understanding of our base 10 system. In our " base 10 blocks " worksheets, students manipulate blocks (units of 1) and rods (groups of 10) to build, deconstruct or add numbers. Later worksheets focus on building or de-constructing multi-digit numbers.

Choose your grade / topic:

Grade 1: Base 10 blocks worksheets

Grade 1: Place value worksheets

Grade 2: Place value worksheets

Grade 3: Place value worksheets

Grade 4: Place value worksheets

Grade 5: Place value worksheets

Topics include:

Grade 1 base 10 blocks worksheets

• Counting and making 10 with ten frames
• Regrouping unit blocks into blocks of 10 ("rods")
• Counting "tens" and "ones"
• Breaking a number (11-99) into rods ("tens") and  blocks ("ones")
• Adding 2 digit numbers with base 10 blocks

Grade 1 place value worksheets

• Identifying tens and ones from 2 digit numbers
• Combining tens and ones into 2 digit numbers
• Identifying a digit's place value (tens, ones)
• Building a 2 digit number with missing addends
• Write 2 digit numbers in expanded form
• Write 2 digit numbers in normal form

Grade 2 place value worksheets

• Building a 3-digit number from the parts
• Missing place values in 3-digit numbers
• Write 3-digit numbers in expanded form
• Write 3-digit numbers in normal form
• Hundreds, tens & ones - identify the underlined digit
• Comparing and ordering numbers up to 100 and 1,000

Grade 3 place value worksheets

• Building 3, 4 and 5-digit numbers from the parts
• Missing place values in 3 and 4-digit numbers
• Write 4-digit numbers in expanded form
• Write 4-digit numbers in expanded notation
• Write 4-digit numbers in standard form
• Identify the place value of the underlined digit
• Compare and order numbers up to 10,000 and 100,000

Grade 4 place value worksheets

• Building 4, 5 and 6-digit numbers from the parts
• Missing place values in 4, 5 and 6-digit numbers
• Write 5-digit numbers in expanded form
• Write 5 digit numbers in expanded notation
• Write 5-digit numbers in standard form

Grade 5 place value worksheets

• Building 5 and 6-digit numbers from the parts
• Missing place values in 5 and 6-digit numbers
• Build numbers from parts with decimals
• Decimal numbers in expanded form
• Decimal numbers in expanded notation

Related topics

Comparing numbers worksheets

Rounding worksheets

Sample Place Value Worksheet

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Place Value Word Problems

Place value in Mathematics describes the position of a digit in a number. Each digit has some value in the number, depending upon its position. When a number is represented in the general form, the position of each digit will be expanded. These positions start from a unit place or ones position. The order of place value of digits in a number from right to left is ones/units, tens, hundreds, thousands, ten thousand, a hundred thousand, and so on. A decimal number can be defined as a number whose whole number part and the fractional part is separated by a decimal point. The dot in a decimal number is called a decimal point. The digits following the decimal point show a value smaller than one. Decimals are based on the preceding powers of 10. Thus, moving from left to right, the place value of digits gets divided by 10. Moving from right to left, the place value of digits gets multiplied by 10.

Harvey has 450 stamps. Mike has 600 stamps. Who has more stamps?

Practice Place Value Word Problems

Practice Problem 1

Practice Problem 2

Practice Problem 3

Place value – is the value of each digit in a number.

Place value chart – The place value chart is a table that is used to find the value of each digit in a number based on its position, as per the numeral system.

Pre-requisite Skills Identify Numbers up to 100 Estimation Order numbers Compare Numbers Place value models Ones tens and hundreds Place Value Models – Up to Thousands

Related Skills Compare Whole Numbers Rounding Whole Numbers to Nearest Thousand Value of Digit – Up to Hundred Thousands Write Numbers for Word Names – Up to Millions Write Word Names for Numbers – Up to Millions Value of Digit – Up to Millions Write Word Names for Numbers Compare Numbers Value of Digits (Decimal Numbers) Write Word Names for Decimal Numbers

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Place Value Problems

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Mastering Place Value: 12 Tips and Strategies for Math Teachers

October 1, 2023 by Debbie Rudtke

Teaching place value to upper elementary students is a crucial milestone in their math education. It lays the foundation for understanding larger numbers, decimals, and more advanced mathematical concepts. To help you make place value engaging and effective for your students, I am sharing some of my favorite tips and strategies. From hands-on activities to real-world applications, these ideas are designed to help your students master place value.

Table of Contents

Place value visual aids.

Visual aids are your allies when teaching place value. They provide students with a tangible representation of abstract concepts, making it easier for them to grasp the fundamentals. Consider using place value charts, base-ten blocks, number lines, and anchor charts to illustrate the relationship between digits and their positional value. You may also choose to create an interactive place value display to show and discuss numbers.

Hands-On Activities

Engagement is key to effective learning. Encourage active participation with hands-on place value activities such as building numbers with base-ten blocks, using an interactive place value bulletin board, matching and sorting task cards, or playing interactive place value games. These activities make learning fun and memorable. Hands-on activities are a great choice for engaging students in math stations rotations while you are working with small groups.

Explore Expanded Form

Introduce students to expanded form, a powerful concept that allows them to break down larger numbers into their constituent parts. For example, 4,732 can be expressed as 4,000 + 700 + 30 + 2. This reinforces their understanding of place value.

Connect with Word Form

Strengthen the connection between place value and word form. Practice reading and writing numbers in word form, such as saying “four thousand seven hundred thirty-two” for 4,732. This helps students relate place value to everyday language.

Comparison Activities

Use comparison activities to illustrate the importance of digits in different place values when comparing numbers. Incorporate symbols like “<,” “>,=” to teach students how to compare numbers effectively.

Real-World Examples

Demonstrate the real-world relevance of place value. Show students how place value plays a crucial role in everyday scenarios, such as reading large numbers on price tags, measuring quantities, or discussing population figures.

Daily Practice

Incorporate daily place value exercises or problem-solving activities into your lesson plans. Consistent practice reinforces place value concepts and helps students retain what they’ve learned. Consider having a “number of the day” activity. Post a number in word form, standard, form, or expanded notation and have students write the number write or show the number in other ways.

Engage With Math Games

Infuse fun and competition into your lessons with math games like “Place Value Bingo,” “Place Value War,” or interactive digital and online games that make learning an enjoyable experience.

Real-World Problem-Solving

Challenge your students with real-world problems that require them to apply their place value knowledge. For instance, calculating change in a store or measuring ingredients in a recipe can provide practical contexts for learning.

Reinforce Vocabulary

Ensure students are familiar with key place value vocabulary, including terms like “digit,” “place,” “value,” “expanded form,” “word form,” “standard form,” and “compare.” Incorporate math vocabulary whenever you are talking to students about numbers such as dates, time, page numbers, money, etc. and encourage your students to do the same!

Teaching place value to upper elementary students can be an exciting journey of discovery. By implementing these tips and strategies in your classroom, you’ll empower your students to master place value, setting them on a path to mathematical success. With the right tools and techniques, you’ll make learning this fundamental math concept fun and memorable for your students.

Looking for more math tips?

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5 Place Value Activities for Deep Understanding

Place Value Lesson #1

Place Value Lesson #2

 When asking students to solve problems like this, encourage them to show their thinking by adding other “benchmark” numbers rather than simply guessing.  Better yet, have them share their thinking so others can learn from different strategies.  This is a great time to identify and clear up place value misconceptions.  Also, this is SO much more powerful than simply filling in the blank on a number line in a workbook!

• Start with numbers lines that do not begin at zero…
• Ask students to identify points outside two numbers on a number line…
• Try having students write their own problems for others to solve…
• Ask students to write about their thinking, not just talk about it…

Place Value Lesson #3

• The number must be a five digit number.
• The first digit must be a 1
• The second digit must be an 8.
• The ones place must be a 1, 3, 5, 7, or 9–until they realize that the tens place number is double the ones place (ruling out the 5, 7, and 9)

Place Value Lesson #4

Place value lesson #5.

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Place-Value Concepts

This page contains resources to support teaching and learning of place-value concepts. Three videos draw on research-based frameworks to illuminate the rich and complex topic of place value and how children come to understand this topic. Additionally an interview protocol for diagnosing student understanding of place value is available along with video examples of students participating in that interview. Finally a list of additional resources is offered for those who wish to go further with study of this topic.

Educator Videos

The following three videos contain a discussion and synthesis of research-based frameworks that can be useful for making sense of student understanding of place-value concepts and an interview protocol in PDF format used to assess students understanding of place value during these interviews.

The Multifaceted Nature of Place Value: It’s About More Than Digit Values

11:56 / View on YouTube / Download Transcript

The Child’s Perspective on Place Value: Five Ways Children Conceptualize Two-Digit Numbers

12:08 / View on YouTube / Download Transcript

Provoking Place-Value Reasoning with Groups of Ten Word Problems: Excerpts from Ms. Brannon’s First Grade Class

14:41 / View on YouTube / Download Transcript

Place-Value Assessment Resources

Click the thumbnails to access resources to support assessment of students’ understanding of place-value in a base-ten number system. The assessment designed to be used in a one-on-one interview setting. Blackline masters are also available in the downloadable file. The downloadable diagram provides a conceptual model for the various components of place-value understanding that occur over a period of several years of school mathematics.

Student Videos

The following three videos show a kindergarten student, a first-grade student, and a second-grade student engaged in the place-value interview.

Kindergarten – Tim

19:51 / View on YouTube / Download Transcript

First Grade – Weston

30:00 / View on YouTube / Download Transcript

Second Grade – Valerie

23:47 / View on YouTube / Download Transcript

Resources for Further Study of Place Value

Click the following titles to access a short list of teacher resource books and journal articles that were reviewed in preparation of these resources.

Teacher Resource Books

• This book details research findings on the development of children’s mathematical thinking in relation to the four operations (addition subtraction multiplication and division) and base-ten number concepts.
• Chapter one of this book includes ideas for teaching and assessing place-value concepts. The book also contains a collection of activities focused on providing children with a variety of experiences generating strategies for organizing large quantities into tens and ones.
• This book includes a collection of ideas for teaching and assessing place-value concepts. Lessons are organized into three main types: Counting and grouping activities number chart activities and activities focused on exchanging ones and tens. The assessments chapter contains suggestions for tasks to use in an individual interview.
• Chapter eleven of this book includes discussion of children’s development of whole-number place-value concepts and ideas for instruction and assessment related to these concepts.
• This article illustrates how contextualized problems involving groups of ten can be used to advance early elementary students’ understanding of place-value concepts.
• This article introduces a set of strategic counting tasks’ to use for the purpose of assessing children’s place-value understanding. The authors discuss the advantages of the strategic counting tasks over other tasks commonly used to assess place-value understanding and detail findings of three research studies that used this set of tasks.
• Drawing on data from four research projects implementing a problem-solving approach to teaching and learning multidigit number concepts and operations this article presents a framework of conceptual structures that articulate different ways children think about multidigit numbers. The article also discusses categories of methods children devise to solve multidigit addition and subtraction problems. The research in this article forms the basis of the ideas presented in  The Child’s Perspective on Place Value: Five Ways Children Conceptualize Two-Digit Numbers (see above).
• This article draws on the work of multiple research projects to identify curricular elements essential for the development of place-value understanding. A framework is suggested for nurturing and assessing place-value understanding in the early elementary grades.
• This article describes findings of two studies utilizing digit-correspondence tasks to explore students’ understanding of the meaning of the digits in two-digit numbers. Implications for the classroom are also discussed.
• This article describes findings from a classroom study that explores the effects of classroom lessons involving digit-correspondence tasks on students’ understanding of the meaning of the digits in two- and three-digit numbers.

Place Value – Definition with Examples

What is place value, place value chart, what is the difference between place value and face value, solved examples on place value, practice problems on place value, frequently asked questions on place value.

In math, every digit in a number has a place value. Place value can be defined as the value represented by a digit in a number on the basis of its position in the number .

For example, the place value of 7 in 3,743 is 7 hundred or 700. However, the place value of 7 in 7,432 is 7 thousand or 7,000. Here, we can see that even though the digits are the same in both numbers, their place value changes with the change in its position. 

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Place Value Chart is a very useful table format that helps us in finding the place value of each digit based on its position in a number. 

The place value of a digit increases by ten times as we move left on the place value chart and decreases by ten times as we move right.  

Here’s an example of how drawing the place value chart can help in finding the place value of a number. 

In the number 13,548

1 is in the ten thousands place and has a place value of 10,000.

3 is in the thousands place and has a place value of 3,000.

5 is in the hundreds and has a place value of 500.

4 is in the tens place and has a place value of 40.

8 is in the ones place and has a place value of 8.

Understanding the place value of digits in numbers helps comparing numbers. It also helps in writing numbers in their expanded form. For instance, the expanded form of the number above, 13,548 is 10,000 + 3,000 + 500 + 40 + 8. 

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Place Value Using Base Ten Blocks

The place value of digits in numbers can also be represented using base-ten blocks and can help us write numbers in their expanded form.

Before, using the base ten blocks to find the place value of each digit in a number, let us first understand what these blocks represent.

Here’s how the number 13,548 can be represented using base-ten blocks.

Decimal Place Value

Decimal numbers are fractions or mixed numbers with denominators of powers of ten . In a decimal number , the digits to the left of the decimal point represent a whole number . The digits to the right of the decimal represent the parts. As we move towards right after the decimal point, the place value of the digits becomes 10 times smaller.

The first digit on the right of the decimal point means tenths i.e. 110. The next place becomes ten times smaller and is called the hunderdths i.e. 1100 and so on. 

In 27.356, 27 is the whole number part, 2 is in tens place and its place value is 20,7 is in ones place, and its place value is 7. 

There are three digits to the right of the decimal point ,               

3 is in the tenths place, and its place value is 0.3 or 3 10

5 is in the hundredths place, and its place value is 0.05 or 5100

6 is in the thousandths place, and its place value is 0.006 or 61000

Place value and face value are not the same. The face value of a digit is the value of the digit, whereas the place value of a digit is its place in the number. In simple words, the face value tells the actual value of the digit, whereas the place value tells the value of the digit based on its position. 

Hence, the face value of the digit never changes irrespective of it’s position in the number. Whereas, the place value of the digit changes with the change in the position. 

For instance, the face value of 2 in both the numbers 283 and 823 is 2. Whereas, the place value of 2 is 200 in 283 and 20 in 823. 

•   What is the place value of 4 in the number 84,527?

The place value of 4 in 84,527 is 4000 (four thousand).

•   Write 412,397 in words using the place value system.

Four hundred twelve thousand three hundred and ninety-seven.

• Write the numbers in figures and in expanded form :
• Ten thousand two hundred and thirty-six
• Seven thousand four hundred and eighty-five
• Ten thousand two hundred and thirty-six = 10,236

= 10,000 + 200 + 30 + 6

• Seven thousand four hundred and eighty-five = 7,485

= 7,000 + 400 + 80 + 5

Place Value

Attend this Quiz & Test your knowledge.

Which digit is at the ten thousands place in the number 783,425?

Select the correct answer in standard form. $40,000 + 4,000 + 200 + 10 + 1$, what will be the place value of 8 in the number 13.86.

Why is understanding place value important?

Place value has its application in many mathematical concepts. It builds the foundation for regrouping , multiplication , etc.

What manipulatives are used to teach place value?

Manipulatives such as base-10 blocks, snap cubes, unifix cubes, beans, etc., are used to develop place value understanding.

Does the place value of a digit increase as it moves from left to right?

No. The place value of a digit decreases by 10 times as it moves from left to right.

What is the difference between the face value and the place value of a digit?

The face value of a digit is the magnitude that it possesses naturally. It is independent of the digit’s position in the number. The place value of a digit depends on its position in the number. For example, the 5 in the number 253 has a face value of 5 and a place value is 50.

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