Place Value in Maths

Place value is the value of a digit based on its position in a number.

In every number, digits have different places such as ones, tens, hundreds, and thousands. The value of a digit changes according to its position and is counted from the right side, starting with the ones place.

Example: Place Value in the number 3846

Place Value Chart

A Place Value Chart is a table that shows the position and value of each digit in a number, such as ones, tens, hundreds, and thousands. We find a digit’s value by checking the column in which it is placed, and large numbers are separated by commas to make them easier to read.

There are two commonly used place value systems:

1. Indian Place Value System

The Indian Place Value Chart is a table that shows the value of each digit according to its position in the Indian numeral system. Large numbers are grouped using commas (like 1,23,456) to make them easy to read and write correctly.

2. International Place Value Chart

The International Numeral System is used worldwide and follows the order of ones, tens, hundreds, thousands, millions, and so on. In this system, commas are placed after every three digits from the right (for example, 135,912,332) to make large numbers easy to read and write.

Place Value Chart with Decimals

The Decimal Place Value Chart shows the value of each digit in a decimal number. A decimal number includes both whole numbers and fractions, separated by a decimal point. The decimal point divides the whole number part (on the left) and the fractional part (on the right).

On the left side, the place values are ones, tens, hundreds, and so on. On the right side, the place values begin from tenths (1/10), then hundredths (1/100), thousandths (1/1000), and so on.

Example: Consider the number 3,467.195

Place Value vs Face Value

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

Also Check

• Number System
• Rational Numbers
• Decimals

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 thousand, 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.