﻿ Place Value, Face Value & Decimal Place Value of a Number

# Place Value, Face Value & Decimal Place Value of a Number

## Place Value of a Number - Sub Topics

• What is Place Value of a Number?
• What is Face Value of a Number?
• Differences between Place Value and Face Value
• Place Values Chart
• Place Value Expanded Form
• Decimal Place Value
• Solved Questions on Place Value of a Number
• Questions to Practice on Place Value of a Number
• The reading material provided on this page for Place Value is specifically designed for students in grades 1 to 6. So, let's begin!

## What is Place Value of a Number?

Face value is the actual value of the digit in a number. For example, if 896 is a number, then the face value of 9 is 9 only, whereas its place value is tens (i.e. 90). Thus, for any number, having a two-digit, three-digit or ‘n’ number of digits, every digit will have a place value and a face value.

For example, in the number 4321, the digit 4 in the thousands place has a value of 4,000, while the digit 1 in the unit place has a value of 1. The place value of a digit determines the overall value of a number, as it helps to identify the magnitude and size of a number. Understanding place value is essential for performing mathematical operations such as addition, subtraction, multiplication and division.

Example:

In the number given 7,256,432

-> The place value of 7 is in the million place and has a value of 7,000,000.

->The place value of 2 is in the hundred thousand place and has a value of 200,000.

->The place value of 5 is in the ten thousand place and has a value of 50,000.

->The place value of 6 is in the thousands of place and has a value of 6,000.

->The place value of 4 is in the hundreds place and has a value of 400.

->The place value of 3 is in the tens place and has a value of 30.

->The place value of 2 is in the ones place and has a value of 2.

So, 7,256,432 = 7,000,000 + 200,000 + 50,000 + 6,000 + 400 + 30 + 2

## What is Face Value of a Number?

Face value is the value of a digit in a number according to its position. For example, in the number 123, the face value of 1 is 1, the face value of 2 is 2, and the face value of 3 is 3.

Examples

Here are some examples of finding the face value of digits in different numbers:

1. In the number 4567, the face value of 4 is 4, the face value of 5 is 5, the face value of 6 is 6, and the face value of 7 is 7.

2. In the number 0.123, the face value of 0 is 0, the face value of 1 is 1, the face value of 2 is 2, and the face value of 3 is 3.

3. In the number 789.01, the face value of 7 is 7, the face value of 8 is 8, the face value of 9 is 9, the face value of 0 is 0, and the face value of 1 is 1.

## Differences Between Place Value and Face Value

 Place Value Face Value Place value refers to the position of a digit within a number. The face value represents the true numerical value of a digit in a number It is determined by multiplying the numerical value of the digit by the corresponding place value. For instance, in the number 852, the place value of 5 is 50 because it occupies the tens place, represented by 10. The face value of a digit is equivalent to its numerical representation. For instance, in the number 852, the face value of the digit 8 is simply 8 itself. The value of a digit in a number is determined by its position or place within that number. The face value of a digit remains consistent and unaffected by its position within a number. The place value of a digit in the ones place is always represented by a single digit. As we move towards the left, each subsequent digit's place value increases by an additional digit. The face value of a digit in a number is represented by a single-digit value.

## Expanded Form of Place Value

Expanded form is a method of writing a number by breaking it down into its individual digits and representing each digit with its place value.

Example: The number 123 can be written in expanded form as 100 + 20 + 3

where;

->100 represents the place value of the hundreds digit (1)
->20 represents the place value of the tens digit (2)
->3 represents the place value of the ones digit (3).

Example: The number 4,567 can be written in expanded form as 4000 + 500 + 60 + 7

where;

-> 4000 represents the place value of the thousands digit (4)
-> 500 represents the place value of the hundreds digit (5)
-> 60 represents the place value of the tens digit (6)
-> 7 represents the place value of the ones digit (7).

## Decimal Place Value

Decimal place value is a system used to represent numbers with fractional parts. It divides the whole number part and the fractional part into different place values. Each place value represents a power of 10.

For example: