Place Value in Mathematics

Place Value in mathematics refers to the value of a digit due to its position or location of a digit within a number, i.e., the place of any digit with respect to decimal. Every digit within a number holds a specific place. When we represent the number in standard notation, the placement of each digit is expanded. This arrangement starts from the rightmost position, known as the unit’s place or one’s position. The sequence of place values, moving from right to left, holds units, tens, hundreds, thousands, ten thousand, hundred thousand, and so forth.

In this article, we will discuss the concept of Place Value in Maths in detail including its definition, properties, formula, and important terminology of Place Value. Other than that, we will also discuss types of Place Value Chart, some solved problems, and provide practice questions for a better understanding of the concept of this article.

Meaning of Place Value

The position of a digit determines the Place Value in a number. Each digit holds a specific value based on its position within the number. It’s important to note that the same digits can have varying place values in a number. The determination of Place Value begins from the right side, known as the one’s position.

Progressing from right to left, the sequence of place values includes ones, tens, hundreds, thousands, tens thousands, and so forth. These values are distinct for each position, ensuring that no two digits within the number share the same value.

Place Value Definition

Place Value is defined as the value of a digit based on its position within a number, denoted by ones, tens, hundreds, and beyond. Every digit in a number possesses a distinct and specific place value. Place Value begins at the rightmost digit, representing units, and then progresses to tens, hundreds, thousands, and so forth, each being a successive power of 10.

For example, consider the digit 5 in the numbers 3258 and 5881. In 3258, the Place Value of 5 is 5 tens or 50. Similarly, in 5881, the Place Value of 5 is expressed as 5 thousand i.e., 5,000. It is important to understand that a digit may be the same, but its value varies according to its position within the number.

How to Find the Place Value?

The Place Value of a digit is determined by its position within a number, ensuring that each digit holds a unique value within the number. To know how place value is determined, we observe that the power of 10, representing the place value, increases by one as we move from right to left in the number.

For example, in the number 326, the unit’s Place Value for digit 6 will be 6 × 10⁰ = 6. Similarly, the tens Place Value for digit 2 will be 2×10¹=20. In the hundreds place, the Place Value for digit 3 will be 3 × 10² = 300.

Properties of Place Value

There are some key properties of place value given below:

• The Place Value of any single-digit number is same to its face value.
• In a two-digit number, the Place Value of the tens digit is ten times the digit itself.
• Place Value is a fundamental principle that a digit’s Place Value is obtained by multiplying the digit by the place value of ‘1’ for the position it occupies.

Place Value Chart

Place Value Charts for numbers help us to ensure proper alignment of digits according to their respective places. These charts provide a clear representation of where each digit should be positioned within a number. To identify the positional values of different digits in a number accurately, we write the individual digits in a number and then utilize a number place value chart to visually inspect their positions. In order to make the process, especially with larger numbers, we divide them into distinct periods separated by commas. Generally, there are two types of place value charts that are widely utilized for this purpose:

• Indian Place Value Chart
• International Place Value Chart

Indian Place Value Chart

The Indian Place Value system operates on a pattern known as 3:2:2. In this system, when dealing with larger numbers, we introduce a comma (,) after the first three digits from the right. Subsequently, commas are placed after every two digits. For example, if we consider the number 2369558, it would be written as 2,36,95,558, following this pattern. Place Value of 3 in the number 2,36,95,558 as 3 ten lakhs or 30,00,000. Then, we refer to a provided table to correctly denote the place values corresponding to each position.

Position of Digit	Place Value	Multiple of 10
9th	Ten Crores	108 = 10,00,00,000
8th	Crores	107 = 1,00,00,000
7th	Ten Lakhs	106 = 10,00,000
6th	Lakhs	105 = 1,00,000
5th	Ten Thousands	104 = 10,000
4th	Thousands	103 = 1,000
3rd	Hundreds	102 =100
2nd	Tens	101 = 10
1st	Ones	100 = 1

International Place Value Chart

This globally accepted Place Value system follows a consistent approach. When dealing with numbers exceeding three digits, a comma (,) is inserted after every set of three consecutive digits, starting from the right. For example, in the case of the number 2369558, we would represent it as 2,369,558. To determine the respective place values, we refer to the provided chart for guidance. The Place Value of 3 in the number 23,695,558 is 3 millions or 3,000,000.

Position of Digit	Place Value	Multiple of 10
9th	Hundred Millions	100,000,000
8th	Ten Millions	10,000,000
7th	Millions	1,000,000
6th	Hundred Thousands	100,000
5th	Ten Thousands	10,000
4th	Thousands	1,000
3rd	Hundreds	100
2nd	Tens	10
1st	Ones	1

Place Value Chart with Decimals

The Decimal Place Value Chart represents the significance of digits in a decimal number, a system that combines whole numbers and fractions through a decimal point. This point divides the whole number portion from the fractional part. While the whole numbers follow the conventional place value chart of ones, tens, hundreds, and so forth, there is a difference in place value for digits to the right of the decimal point. 

As we move to the right after the decimal point, the place values initiate from tenths, then proceed to hundredths, thousandths, and so forth. Following a Place Value Chart for Decimal numbers provides a clear understanding of these values.

Place Value and Face Value

A number is constructed by arranging digits in specific groupings.

• Every digit is assigned a distinct position, known as its “Place.”
• Each digit has a value depending on its place called the Place Value of the digit.
• The “Face Value” of a digit for any place in the given number is the value of the digit itself.
• The Place Value of a digit can be calculated by multiplying its face value by the numerical value of its place.

Difference Between Place Value and Face Value

The key differences between Place Value and Face Value in math is listed below:

Place Value	Face Value
The position a digit holds within a number determines its Place Value.	The Face Value represents a digit’s actual numerical value within a number.
The Place Value depends upon the digit’s location within the number.	It remains constant regardless of the digit’s placement in the number.
In the units place, a digit’s Place Value is a single digit, and as we move left, each subsequent digit’s place value increases by a factor of 10.	The Face Value of any digit is always a single digit.

Read More,

• Number Sysmtem
• Rational Numbers

Solved Examples on Place Value

Example 1: Determine the Place Value of the digit 5 in the number 84,520.

Solution:

In the number 84,520, the digit 5 holds a Place Value of 500, specifically, five hundred.

Example 2: Express the given numbers in both numerical and expanded forms:

• Ten thousand two hundred and thirty-six
• Seven thousand four hundred and eighty-five

Solution:

For “Ten thousand two hundred and thirty-six”:

In numerical form: 10,236

In expanded form: 10,000 + 200 + 30 + 6

For “Seven thousand four hundred and eighty-five”:

In numerical form: 7,485

In expanded form: 7,000 + 400 + 80 + 5

Example 3: Given a number with 8 thousands, 7 hundreds, and 8 tens, determine the number.

Solution:

We calculate the Place Value for the respective digits as follows:

8 thousands = 8,000

7 hundreds = 700

8 tens = 80

Adding all Place Value, we obtain: 8,000 + 700 + 80 = 8,780. Hence, the number is 8,780.

Example 4: Determine the Place Value of the digit 2 in the number 4.32.

Solution:

Using the Decimal Place Value Chart, we identify that the Place Value of 2 in 4.32 corresponds to 2 hundredths. This can be precisely expressed as 2/100, which is equivalently represented as 0.02.

Practice Questions on Place Value

Question 1: Identify the digit situated at the place value of ten thousand within the number 883,425.

Question 2: Determine the specific Place Value of the digit 8 in the number 15.86.

Question 3: Determine the Place Value for the underlined digits in the provided spaces.

• In the number 6,103
• In the number 7,00,495
• In the number 8,15,824
• In the number 2,18,651

Question 4: Calculate the Place Values for each digit within the number 2651.325.

Question 5: Compute the Place Values for every digit in the number 76014 and proceed to represent it in an expanded form.

Place Value – FAQs

1. What does “Place Value” refer to?

Place Value is defined as the value of a digit based on its position within a number, denoted by ones, tens, hundreds, and beyond. Every digit in a number possesses a distinct and specific place value.

2. How can we determine the Place Value of a digit?

To determine the Place Value of a digit, we must recognize that the value of each digit depends on its position within a number. For example, the Place Value of ‘6’ in 3468 is 6 tens, or 60. Similarly, in 6781, the place value of ‘6’ is six thousand or 6,000.

3. Can you provide examples of Place Value in numbers?

Yes. Place Value signifies a digit’s value within a number. Here are a few examples:

The Place Value of ‘2’ in 24 is 2 × 10 = 20.

For the number 543, the Place Value are as follows: ‘5’ is in the hundreds place, 5 × 100 = 500; ‘4’ is in the tens place, 4 × 10 = 40; ‘3’ is in the ones place, 3 × 1 = 3.

4. Define a “Place Value Chart”

Place Value Charts for numbers help us to ensure proper alignment of digits according to their respective places. These charts provide a clear representation of where each digit should be positioned within a number.

5. How can we create a Place Value Chart?

Creating a Place Value Chart involves these steps:

Step 1: Draw columns representing various periods according to the numeral system, such as ones, tens, hundreds, thousands, and so on.

Step 2: Below each period, set up sub-columns to display the distinct Place Values.

Refer to the Indian and International Place Value Charts to understand the layout for different numeral systems.

6. Why is Place Value in Numbers Important?

The concept of Place Value in numbers is important because it gives the worth of every digit based on its position within a number. It is the foundation for understanding comprehending the numerical knowledge of Place Values.

7. What is the Place Value of zero?

The Place Value of zero is always zero. In a number like 4077, where zero appears in the hundreds place, its Place Value is expressed as 0 hundreds, resulting in 0 × 100 = 0.

8. How does the Place Value of a digit change as we move from right to left?

The Place Value of a digit increases tenfold as we moves from right to left in a whole number.

9. How does Place Value differ from face value?

Place Value signifies a digit’s position within a number and its associated value, while face value represents the digit’s exact value regardless of its position within the number. For example, in the number 2004, the place value of ‘2’ is in the thousands place, whereas the face value remains 2.

10. Why is understanding Place Value important?

Place Value finds application in numerous mathematical concepts, serving as a fundamental principle for regrouping, multiplication, and other essential mathematical operations. It is foundational to understanding and working with numbers effectively.