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Nikita Parmar

Updated on 29th August, 2023 , 6 min read

What is the Difference between Place Value and Face Value?

Place Value and Face Value Introduction

The primary distinction between place value and face value is that the place value deals with the digit's location, whereas the face value indicates the real value of a digit. The number system is provided and is required for classifying digits into groupings of tens, hundreds, and thousands.

Place Value and Face Value Definitions

With the use of an enlarged form of a number, the notion of face value and place value of a digit may be better understood. 

For Example: 842 = 800 + 40 + 2

                                = 8 × 100 + 4 × 10 + 2 × 1

The following table shows the enlargement of place and face value- 

Digits

Place Value 

Face Value 

8

800

8

4

40

4

2

2

2

The above table provides the solution to the question: What is the face value and place value of a digit in a number?

Face Value

Any number's face value can be expressed as the value of the digit itself. Place value refers to the value of each digit in a number. We calculate a number's place value by multiplying its digit value by its numerical value. 

For Example: Find the face value of each digit in the number 4856.

Solution: Every digit's face value is the number itself.

The face value of '4' is four.

The face value of '8' is eight.

The face value of the number '5' is five.

The face value of the number '6' is six.

Place Value

The position of a digit in a number is represented by its place value. Determine the place value of each digit in the integer 4856. To determine the place value of the numbers in the number 4856, multiply each number by the digit value. 

  1. Since 4 is in the thousands place, the place value of 4 can be computed by multiplying 4 (numerical value) by 1000 (digit value), resulting in 4 x 1000 = 4000. Similarly, we can determine the place values for the remaining digits in the number. 
  2. Because 8 is in the hundreds place, the place value of 8 may be computed by multiplying 8 by 100, resulting in 8 x 100 = 800.
  3. Because 5 is in the tens place, the place value of 5 may be computed by multiplying 5 by 10.
  4. 6's place value may be computed by multiplying 6 by 1, that is, 6 x 1 = 6 because 6 is in the first place.

Expanded Form of Place Value and Face Value

The distinction between place value and face value is made using the extended form of a number. 5689 in its enlarged form equals 5000 + 600 + 80 + 9. In the extended form, we express a number as the sum of the place values of each individual digit. The place value of 5 in the number 5689 is 5000 (since 5 is in the thousands place), the place value of 600 (since 6 is in the hundreds place), the place value of 8 is 80, and the place value of 9 is 9. (since 9 is in ones place). However, the face value of 5 in the same number 5689 is 5, the face value of 6 is 6, the face value of 8 is 8, and the face value of 9 is 9.

Properties of Place Value

The following are the properties of place value-

  1. Every one-digit number's place value is the same as and equal to its face value.
  2. The place value of the tenth digit in a two-digit number is ten times the digit.
  3. The digit 5 is at one, the digit 7 is at ten, and the digit 4 is at hundred in the number 475.
  4. The basic rule is that the digit has its place value as the product of the digit and the place value of one to be in that location.

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What is the difference between Place Value and Face Value?

The number system in place means values range from 0 to tens, hundreds, thousands, and so on. The following table gives more information about the key distinctions between place value and face value-

Place Value 

Face Value 

The place value describes the position or place of a digit in a given number. 

The digit itself within a number is simply defined as having a face value.

For Example- The place value of 5 in the number 452 is (5 10) = 50 because 5 is in the tens place. 

For Example- The face value of 6 in the number  360 is 6.

Place Value = Face Value x numerical value of place.

Face value of digit = numerical value of the digit itself.

The place value of 0 is 0.

The place value of 0 is 0.

To get a number's place value, multiply its digit value by its numerical value.

The face value of a digit is always the same, regardless of where it is positioned.

The value indicated by a digit in a number based on its position in the number is known as place value.

The face value of a digit in a number is its real value and is independent.

Chart of Place Value and Face Value

When reading numbers, it is usually easier to use words than individual digits. For example, instead of reading 527 as 5, 2, 7, it is simple to read 527 as five hundred and twenty-seven. There are two frequently used numeration methods, which are as follows-

The Indian System of Numeration

The Vedic numbering system is the foundation of the Indian numeration system. For this one must divide the provided integers into groups or periods. Students must begin with the extreme right digit of the supplied number and work their way to the left. 

  1. The first three numbers are on the far right. The digits in one column are divided into hundreds, tens, and units. 
  2. The group of thousands is formed by the second group of the following two digits to the left of the group of ones, which is further divided into thousands and ten thousand. 
  3. The third group of two numbers to the left of the group of thousands forms the group of lakhs, which is split into lakhs and ten lakhs. The two digits on the left side of the lakhs then add up to a crore split into crores and ten crores.

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The International System of Numeration

The International System of Numbers is used by the majority of the world's countries. The total is split into groups or periods in this approach. To form the groups, one must begin with the number's extreme right digit. The various groups are referred to as the ones, thousands, millions, and billions. The digits in one column are divided into hundreds, tens, and units. The following three numbers on the left side of the group of ones form the group of thousands, which is further subdivided into thousands, ten thousand, and a hundred thousand. The group of millions is formed by the third group of the following three numbers on the left side of the group of thousands. Three numbers on the left side of the million groups create the billion group, which is split into billions, ten billion, and hundred billion. 

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Things to Keep in Mind

  1. The place value and face value of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 are 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively.
  2. The face and place value of 0 is always zero.
  3. Any digit's face value always remains constant.
  4. A digit's place value is calculated by multiplying it by 10n, where n is the digit's position in the number from the right side.
  5. The extended form assists in determining the place value of each digit in the provided integer.

Solved Examples of Place Value and Face Value

Example 1: Find the Place and Face values for each digit in the number 4657.

The following table shows the place value and face value of the digits-

Digits

Place Value 

Face Value 

6

6000

6

2

200

2

3

30

3

4

4

4

As a result, these are some of the fundamental distinctions between face value and place value. It is critical to understand the differences between the two because they are both utilized in mathematical expressions to solve and compute. 

Conclusion 

A number's place value is defined as the position or location of a digit inside the number. Any number's face value can be expressed as the value of the digit itself. Various systems, such as the Indian system of numeration and the International system of numeration, can be used to compute the place and face value. The numbers are split into groups or periods in the International method of enumeration. Every digit of a number has a face and a place value in the Indian system of numeration. The digit's place value is determined by its location. The location of the digit has no bearing on the face of the digit.

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Frequently Asked Questions

Ans. The face value of a digit in a number determines the number’s value. It makes no difference what position the digit is in. For example, the face value of 9 in 911 is simply 9.

Ans. 2 in 93207 has a face value of 2.

Ans. A digit’s place value in a number determines where it is put or positioned. It may be in the first place, the tenth place, the hundredth position, and so on. For example, the place value of 5 in 252 is 5 x 10 = 50, which is the tenth place.

Ans. The place value of 6 in 6391 is 6000.

Ans. Many mathematical ideas make use of place value. It lays the groundwork for regrouping, multiplication, and other operations.

Ans. To enhance place value comprehension, manipulatives such as base-10 blocks, snap cubes, unfix cubes, beans, and so on are employed.

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