Place value and face value are the most important parameters in mathematics. These two are the basic pillars of mathematics. Let’s welcome to our session to understand all the basic ideas!

What is Place Value?

Place value is related to the position or place, as the name suggests. We come across various numbers all the time. Numbers consist of digits. It may be one digit or 2 digits of 3 digits or many more. Now, each digit has a position in the number. Depending on that position or place, each digit has a value. This value is known as the place value.

Place Value Definition

It is defined as the position of each digit in any number.

Explanation

We all know counting from 0 to 9 and these are the main numbers which we use to express all other numbers. Now, you have been given so many numbers of balls and assigned a few containers or places from your right side to the left side. Let’s consider a few buckets or say ‘places’, like;

Place-7	Place-6	Place-5	Place-4	Place-3	Place-2	Place-1

Remember,

• You have to go from right to left.
• Your task is to fill the place.
• Each place will contain only one digit.

Let’s start,

• You start with place 1 and only one digit can be placed here and there are no digits on the right side. So, this place-1 is called ones.
• Now, after 9 balls, the first place is filled and you need to go for second place, as 10 is having two digits. So, second place is started at 10 where 1 is in the place-2 and 0 is in place-1. This place-2 is called tens.
• When you are keeping 99 balls, the next ball requires 3rd place. So, third place is started at 100 where 1 is in the place-3 and 0 is in place-2&1. This place-3 is called hundreds. This process is going on.

From these examples, we can see that,

• Place 1 refers to 1 digit numbers i.e ones (1).
• Place 2 refers to 2 digit numbers i.e tens (10).
• Place 3 refers to 3 digit numbers i.e hundreds (100).
• Place 4 refers to 4 digit numbers i.e thousands (1000) and so on.

The value of balls can contain in an individual place, is simply place value.

Take any number, 765.

Here, a place value of 6 needs to find out.

So, 6 is in 2^nd place and we will simply say 6 tens or 6 multiply by10 = 6 x 10 = 60.

How to calculate Place Value?

• This value is calculated by multiplying the digit with the value of its place or position.
• It is determined as ones, tens, hundreds, thousands, ten thousands, millions, ten-millions, etc. based on the digit’s place.

Place Value Example

Let us try to see some examples,

• 75649: Place value of 6 in 75649 is 6 hundred or 6×100 = 600.
• 5245: Place value of 5 in 5245 is 5 thousand or 5 X 1000 = 5000.
• 5489: Place value of 8 in 5489 is 8 tens or 8 X 10 = 80.

Place Value Chart

Place value chart is the basic chart by which we can easily place the digits in the proper places.

• Now, how to use this chart?
• Is it applicable for whole numbers and decimal numbers?

Let’s learn the place value chart for whole numbers and decimal numbers.

• Place value chart implies the value of each digit,
• It also implies how many ones, tens, hundreds, needs to use,

Steps to use place value charts,

• Write the place value chart.
• Then write the digits in the place value chart.
• Write the numbers normally.

Place value charts are used for two systems,

• International Place Value Chart
• Place value chart for Indian system

Place Value Chart for Whole Numbers

International System

Indian System

Value of a digit = digit x place value.

Refer to the below table for a basic concept of the place value of a digit and the value of a digit.

Indian System & International System Comparison

In both systems, 5-digit numbers are read in the same way.

Let’s see a simple comparison table to read the numbers in both the systems.

No. of. Digits	International System	Indian System
1-Digit Numbers	One (1)	One (1)
2-Digit Numbers	Ten (10)	Ten (10)
3-Digit Numbers	Hundred (100)	Hundred (100)
4-Digit Numbers	Thousand (1000)	Thousand (1000)
5-Digit Numbers	10 Thousand (10,000)	10 Thousand (10,000)
6-Digit Numbers	100 Thousand (100,1000)	1 Lakh (1,00,000)
7-Digit Numbers	1 Million (1,000,000)	10 Lakhs (10,00,000)
8-Digit Numbers	10 Million (10,000,000)	1 Crore (1,10,00,000)
9-Digit Numbers	100 Million (100,000,000)	10 Crores (10,00,00,000)

Place Value Chart with Decimals

Decimal numbers mean we all know that simply fractions or a number with denominators of power of ten.

• Any decimal number has two parts,
• The left side of the digit is the whole number,
• The right side of the decimal point is simply parts,
• Place value of the digit is 10 times smaller,

Place value chart of decimals are as follows,

The first digit on the right of the decimal point means tenths. The second digit on the right of the decimal point means hundreds. The third digit on the right of the decimal point means thousands. Let’s us consider a decimal number, 84.5912

• 84 is the whole number part,
• 8 is in tens place and its place value is 80,
• 4 is in ones place, and its place value is 4.
• There are four digits to the right of the decimal point,
• 5 is in the tenths place after decimal point, and its place value is 0.5,
• 9 is in the hundredths place after decimal point, and its place value is 0.09,
• 1 is in the thousandths place after the decimal point, and its place value is 0.001,
• 2 is in the ten thousandths place after the decimal point, and its place value is 0.0002,

There are various types of worksheets available on the internet for practice.

What is Face value?

Face value means the value of the digit itself in any number.

Face Value Example

Let us try to see place value examples,

• 5362: Face value of 6 is 6.
• 5456: Face value of 4 is 4.
• 9802: Face value of 8 is 8.
• 9325: Face value of 9,3,2,5 is 9,3,2,5 respectively.

There is a relation between place value and face value. We will see it with examples, Number 35487 Let’s find the place value and face value of 3. Face value of 3 is 3. Here, the position of 3 is 10000, and the face value of 3 is 3. Place value of 3, will be 3 x 10000 i.e. 30000.

Hence, we can say,

Place value = Face Value x Position

Check out a nice VIDEO form Mathantics,

Place Value Table

International System

Refer Place value in international system,

Number	Place Value
728,529,674	Place value of 4 in 728,529,674 = 4
728,529,674	Place value of 7 in 728,529,674 =70
728,529,674	Place value of 6 in 728,529,674 = 600
728,529,674	Place value of 9 in 728,529,674 =9,000
728,529,674	Place value of 2 in 728,529,674 = 20,000
728,529,674	Place value of 5 in 728,529,674 = 500,000
728,529,674	Place value of 8 in 728,529,674 = 8,000,000
728,529,674	Place value of 2 in 728,529,674 = 20,000,000
728,529,674	Place value of 7 in 728,529,674 = 700,000,000

Indian System

Let’s see the place value of every digit in the below number,

Number	Place Value
21,34,56,197	Place value of 7 in 21,34,56,197 = 7
21,34,56,197	Place value of 9 in 21,34,56,197 = 90
21,34,56,197	Place value of 1 in 21,34,56,197 = 100
21,34,56,197	Place value of 6 in 21,34,56,197 = 6,000
21,34,56,197	Place value of 5 in 21,34,56,197 = 50,000
21,34,56,197	Place value of 4 in 21,34,56,197 = 4,00,000
21,34,56,197	Place value of 3 in 21,34,56,197 = 30,00,000
21,34,56,197	Place value of 1 in 21,34,56,197 = 1,00,00,000
21,34,56,197	Place value of 2 in 21,34,56,197 = 20,00,00,000

Difference Between Place Value and Face Value

We have already got the basic idea of place value and face value. Now, we will see the differences between place value and face value.

Sl. No.	Place Value	Face Value
1	Place value is used to find out the value of the position of any digit in any number	Face value means the value of the digit itself in any number
2	Place value is equal to the multiplication of Face value and the value of the position of the particular digit	Face value is equal to the numerical value of the digit only
3	Place value depends on the position of the digit in the number	It is independent on the position

It will be easy to differentiate with an example, let us take a number, 5427.

Digits	Place Value	Face Value
5	5 Thousands	5
4	4 Hundreds	4
2	3 Tens	2
7	7 Units or ones	7

Place Value & Face Value Examples

Number 75649

Digits	Place Value	Face Value
7	7 x Ten Thousands = 70 Thousands = 70,000	7
4	4 x Thousands = 4 Thousands = 4,000	4
6	6 x Hundreds = 6 Hundreds = 600	6
4	4 x Tens = 4 Tens or 40	4
9	9 x Units or ones = 9 Ones or 9	9

Number 84396

Digits	Place Value	Face Value
8	8 x Ten Thousands = 80 Thousands = 80,000	8
5	5 x Thousands = 5 Thousands = 5,000	5
3	3 x Hundreds = 300	3
9	9 x Tens = 9 Tens = 90	9
6	6 x Units or ones = 6 Ones = 6	6

Solved Example

Write the number 562,736,914,235 in the international system and 49187235 in the Indian system.

Solution:

So, how to write? We have already learned the chart for the international system, and we will write all the digits based on that chart,

Now, based on the Indian system chart, we can write 4,91,87,235 as bellow,

Conclusion

Hence, we have learned the basics of place value along with the chart, face-value along with writing digits in the chart. We have seen many examples and how a single number can be written in the International system and Indian systems. Please write to us, if you have any doubts.

Further Study