Place Value Chart: Definition, Example, Printable PDF

Understanding place value is essential for anyone learning math. It refers to how the position of a digit in a number determines its value. Whether you’re working with whole numbers or decimals, grasping this concept is key to interpreting and using numbers effectively. A place value chart can help visualize this idea, showing how each digit contributes to the overall value.

In this article, we’ll define place value, share some practical examples, and provide a printable PDF chart for easy reference. This resource aims to make it simpler for you to understand and apply place value in your math studies.

Place Value Chart

A place value chart is a helpful visual tool that shows how much each digit in a number is worth based on its position. It organizes numbers into columns for ones, tens, hundreds, thousands, and more. Each column represents a power of 10, meaning the value of a digit changes depending on where it is placed in the chart. This makes it easier to understand and work with numbers.

Place Value Chart in Indian System

The Indian system of numeration organizes numbers in a unique way that differs from many other systems. In this system, numbers are grouped into periods, starting with the first three digits (ones, tens, and hundreds). After that, the grouping continues in pairs of two digits. This means that the next set of values includes thousands, ten thousands, lakhs, and crores.

This system not only makes it easier to read and write large numbers but also helps in understanding the value of each digit based on its position.

Indian place value chart:

Crores	Ten Lakhs	Lakhs	Ten-Thousands	Thousands	Hundreds	Tens	Ones
1,00,00,000	10,00,000	1,00,000	10,000	1,000	100	10	1

Place Value Chart in International System

The foundation of our entire number system is place value, which is based on a pattern of tens. The International System groups numbers into periods of three digits (ones, thousands, millions, billions, etc.). It does not use terms like lakhs or crores.

In this system, each group of three digits is separated by commas, which helps in reading and writing numbers more clearly. For example, one thousand is represented as “1,000,” one million as “1,000,000,” and one billion as “1,000,000,000.”

Unlike the Indian System, the International System does not use terms like lakhs or crores. Instead, it relies on a consistent framework that is widely recognized and used in many countries around the world.

International Place Value Chart:

Billions	Hundred Millions	Ten Millions	Millions	Hundred Thousands	Ten Thousands	Thousands	Hundreds	Tens	Ones
1,000,000,000	100,000,000	10,000,000	1,000,000	100,000	10,000	1,000	100	10	1

Decimal Place Value Chart

A decimal place value chart represents the value of digits in a decimal number. Decimal numbers consist of two parts: the digits to the left of the decimal point represent the whole number part of the decimal number. The digits to the right of the decimal point represent the fractional part of the number.

Each digit in a decimal number has a specific place value based on its position relative to the decimal point.

Example: Decimal Number 345.678

Let’s break down the decimal number 345.678 using the place value table:

Place Value	Digit	Calculation	Value
Hundreds	3	3×100	300
Tens	4	4×10	40
Ones	5	5×1	5
Decimal Point	.	–	–
Tenths	6	6×0.1	0.6
Hundredths	7	7×0.01	0.07
Thousandths	8	8×0.001	0.008

So, 345.678 = 300+40+5+0.6+0.07+0.008.

Difference Between Place Value and Face Value

• Face Value: The face value of a digit is the value of the digit itself, irrespective of its position in a number. For example, in the number 547, the face value of the digit ‘5’ is 5, the face value of ‘4’ is 4, and the face value of ‘7’ is 7.
• Place Value: The place value of a digit is determined by its position in a number. It is calculated by multiplying the face value of the digit by the value of its place (which is a power of 10). For example, in the number 547, the place value of ‘5’ is 5 × 100 = 500, the place value of ‘4’ is 4 × 10 = 40, and the place value of ‘7’ is 7 × 1 = 7.

Let us take an example of the number 6825. Check the table below to understand the difference.

Digits	Place Value	Face Value
6	Thousands	6
8	Hundreds	8
2	Tens	2
5	Units or ones	5

Place Value Chart PDF

When teaching place value within the decimal system, using a printable place value chart can be extremely helpful. The chart shows the various number places, from the ten thousandth place on the left-hand side for whole numbers to the thousandth place on the right-hand side for decimal fractions.

For example, consider a two-digit number like 23. In this number, the digit 2 in the tens place represents two sets of ten, which can be thought of as two ten-blocks (since ten ones make one ten).

Students, on the other hand, can refer to it while doing their homework, helping them internalize the concept of place value. Moreover, the PDF format allows for easy customization.

Place value chart printable

A blank place value chart is useful for helping students practice and visualize the value of digits in various numbers, enhancing their understanding of place value concepts. the numbers should be in order, and the numbers should be in the correct position. As you assess each child, check the placement of the written numbers.

Solved Examples of Place Value

Understanding place value is a cornerstone of numeracy. It forms the basis for operations like addition, subtraction, multiplication, and division. One of the most effective ways to visualize and grasp this concept is through the use of place value blocks. These physical or virtual manipulatives represent different place values, such as ones, tens, hundreds, and thousands, allowing students to build and break down numbers.

These examples will not only rely on the theoretical understanding of place value but also demonstrate how place value blocks can be used as a practical tool to solve numerical challenges.

Example 1:

Write the number 47,286,523 in the International Place Value System, including commas and its written form in words.

Solution:

MILLION		THOUSANDS			ONES
T.M	M	H.Th	T.Th	Th	H	T	O
4	7	2	8	6	5	2	3

1. Writing the number with commas:

• In the International System, we group the digits in sets of three, starting from the right. So, 47286523 is written as 47, 286, 523.

2. Writing the number in words:

• We start from the left-most group.
• Write the 47, 286, 523 in expanded form: forty-seven million, two hundred eighty-six thousand, five hundred twenty-three.

​Example 2:

In the number 5679012, write the digit that is in
(a) thousands place
(b) millions place
(c) ten’s place
(d) hundred’s place

Solution:

(a) A number in thousands place is 9
(b) A number in millions place is 5
(c) A number in ten’s place is 1
(d) A number in hundred’s place is 0

Example 3:

Write the place value of the underlined digit: 382

Solution:

When we talk about the place value of 8 in 382, we can think of it in terms of “how many tens” it represents. Since 8 is in the tens place, the place value of 8 in 382 is 8 tens. This means the place value of 8 is expressed as 8 × 10 = 80.

Conclusion

Mastering place value is fundamental to understanding mathematics, as it serves as the foundation for various arithmetic operations and concepts. A place value chart not only clarifies the value of digits in numbers but also enhances comprehension of larger numbers and decimals. By visualizing how each digit contributes to the overall value, learners can approach mathematical problems with greater confidence and accuracy.

Online math courses provide the opportunity for students to dive deeper into place value and other fundamental mathematical concepts.

FAQs

Q1: How do you explain a place value chart?

A place value chart is a visual representation that shows the value of each digit in a number based on its position. Starting from the right – most digits, the positions are ones, tens, hundreds, thousands, and so on. Each position has a value that is a power of 10.

For example, in the number 345, the digit 5 is in the one’s place with a value of 5 (since 5 × 1 = 5), the digit 4 is in the tens place with a value of 40 (4 × 10), and the digit 3 is in the hundreds place with a value of 300 (3 × 100). It helps in clearly understanding the structure of numbers and is crucial for various arithmetic operations.

Q2: How do you find the value of a place?

The value of a place is determined by the position of the digit within the number. Each place has a base – 10 value. The ones place has a value of 10° = 1, the tens place has a value of 10¹ = 10, the hundreds place has a value of 10² = 100, the thousands place has a value of 10³ = 1000, and so on.

To find the value of a digit in a particular place, you multiply the digit by the value of that place. For instance, in the number 729, the digit 2 is in the tens place, so the value of the digit 2 in this number is 2 × 10 = 20.