# Place Value

The place value of a digit in a number is the value it holds to be at the place in the number. We know about the place value and face value of a digit and we will learn about it in details.

We know that each digit in a number has a place. The place that a digit occupies in a number tells us about its place value.

Let us take a 3-digit number 915

 915 = 9 hundreds 1 ten and 5 ones. We note that the digit 9 in the number 915 is at hundreds place.

So, the place value of digit 9 is 9 hundred or 900.

The place value of digit 1 is 1 ten or 10.

The place value of digit 5 is 5 ones or 5.

Place, Place Value and Face Value:

A number is formed by grouping the digits together.

● Each digit has a fixed position called 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

● Place value of a digit = (face value of the digit) × (value of the place)

We know that each digit in a number has a place value. The place a digit occupies in a number tells us its place value. So, the product of the digit and the value of the place it occupies gives us the place value. Let us arrange the digits of the number 5, 32,161 in the following place value chart.

The face value of a digit in a number is the digit itself.

Properties of Place Value:

1. The place value of every one-digit number is the same as and equal to its face value.

(i) Place value and face value of 1, 2, 3, 4, 5, 6, 7, 8 and 9 are 1, 2, 3, 4, 5, 6, 7, 8 and 9 respectively.

(ii) The place value of zero (0) is always 0. It may hold any place in a number, its value is always 0.

As, in 105, 350, 42017, 90218 the place value of 0 in each number is 0.

2. In a two-digit number, the place value of the ten-place digit is 10 times of the digit.

As, in 58, the place value of 5 is 5 × 10 = 50 and place value of 8 is 8 × 1= 8; the face value of 5 is 5 and of 8 is 8.

3. In the number 475, the digit 5 is at one’s place, digit 7 is at ten’s place and digit 4 is at hundred’s place.

So, place value of 5 = 5, place value of 7 = 7 × 10 = 70, and place value of 4 is 4 × 100 = 400.

Thus, for the place value of a digit, the digit is multiplied by the place value of 1 it has to be that place.

For Example:

In 768;

the place value of 8 = 8 × 1 = 8

the place value of 6 = 6 × 10 = 60 and

the place value of 7 is 7 × 100 = 700.

4. Now it is the general law that the digit possesses its place value as the product of the digit and place value of one to be at that position.

For Example:

(i) In a number 4129;

the place value of 9 is 9 × 1 = 9 as 9 is at one’s or unit’s place.

the place value of 2 is 2 × 10 = 20 as 2 is at ten’s place.

the place value of 1 is 1 × 100 = 100 as 1 is at hundred’s place.

the place value of 4 is 4 × 1000 = 4000 as 4 is at thousand’s place.

(ii) In a number 3720, the place value of

 3 is 3 × 1000 = 30007 is 7 × 100 = 7002 is 2 × 10 = 20 0 is 0 × 1 = 0 3 being at Th-place7 being at H-place2 being at T-place0 being at one’s or unit’s place

(iii) Place value of the digits 3702 are shown below:

(iv) Here, we also see that the place value of the digit 0 in a number is always zero, whatever may be its position.

Place-value of a Digit in a Number:

We know that the position of a digit in a number determines its corresponding value in the number. Let us consider the number 64,19,85,062 and write place-value of each digit in the following chart.

We read the above number as thirty-four crore, nineteen lakh, seventy-five thousand, fifty-two.

Solved Examples Place-value of a Digit in a Number:

1. Write the place-value of 5 in the given numbers:

(i) 50,21,38,761

(ii) 82,05,36,401

(iii) 79,46,15,380

Solution:

Let us arrange the digits in the place-value chart

(i)

Place value of 5 in the number is

5 × 10,00,00,000 = 50,00,00,000. It is read as fifty crore.

(ii)

Place value of 5 in the number is

5 × 1,00,000 = 5,00,000. It is read as five lakh.

(iii)

Place value of 5 in the number is

5 × 1,000 = 5,000. It is read as five thousand.

2. Write the place value of underlined digits in the given blank.

(i) 5,103

(ii) 7,00,496

(iii) 8,15,924

(iv) 2,18,951

Solution:

(i) 5,103

3 being at one’s or unit’s place

The place value of 3 in the number 5,103 is 3.

(ii) 7,00,496

7 being at Lakhs-place

The place value of 7 in the number 7,00,496 is 7,00,000.

(iii) 8,15,924

2 being at Tens-place

The place value of 2 in the number 8,15,924 is 20.

(iv) 2,18,951

2 being at Lakhs-place

The place value of 2 in the number 2,18,951 is 2,00,000.

3. Circle the following.

(i) Digit at lakhs place - 17,45,015

(ii) Digit with face value of 9 - 49,00,781

(iii) Digit at ten crores place - 92,15,55,470

(iv) Digit at ten thousands place - 75,19,778

(v) Digit at tens place - 92,15,55,470

Solution:

(i) 7

(ii) 9

(iii) 9

(iv) 1

(v) 7

4. Find the place value of 9 in the given numbers.

(i) 6,96,242

(ii) 3,29,162

(iii) 4,52,921

We first arrange the digits of the given number in the place value chart.

(i) Place value of 9 in the number 6,96,242 is

9 × 10,000 = 90,000

(ii) Place value of 9 in the number 3,29,162 is

9 × 1,000 = 9,000

(iii) Place value of 9 in the number 4,52,921 is

9 × 100 = 900

5. Write the place value of the digit underlined in each number.

(i) 67843

(ii) 765432

(iii) 865409

(iv) 736524

(v) 800026

6. Rewrite using the Indian place-value chart and write the number name.

(i) 364,875

(ii) 42, 760, 542

(iii) 6,521,324

7. Rewrite using the International place-value chart and write the number name.

(i) 7,24,60,542

(ii) 21,56,324

(iii) 2,83,964

Math Only Math is based on the premise that children do not make a distinction between play and work and learn best when learning becomes play and play becomes learning.

However, suggestions for further improvement, from all quarters would be greatly appreciated.

Related Concept

## You might like these

• ### Factors | Understand the Factors of the Product | Concept of Factors

Factors of a number are discussed here so that students can understand the factors of the product. What are factors? (i) If a dividend, when divided by a divisor, is divided completely

• ### Formation of Numbers | Smallest and Greatest Number| Number Formation

In formation of numbers we will learn the numbers having different numbers of digits. We know that: (i) Greatest number of one digit = 9,

• ### Place Value Chart | Place Value Chart of the International System

In place value chart, the digits are grouped in the threes in a big number. The number is read from left to right as … billion …million …. thousands …ones. The place value chart of the International System is given below: Place Value Chart 100,000 = 100 thousand 1,000,000

• ### Examples on the Formation of Greatest and the Smallest Number |Example

In examples on the formation of greatest and the smallest number we know that the procedure of arranging the numbers in ascending and descending order.

• ### Arranging Numbers | Ascending Order | Descending Order |Compare Digits

We know, while arranging numbers from the smallest number to the largest number, then the numbers are arranged in ascending order. Vice-versa while arranging numbers from the largest number to the smallest number then the numbers are arranged in descending order.

• ### Comparison of Numbers | Compare Numbers Rules | Examples of Comparison

Rule I: We know that a number with more digits is always greater than the number with less number of digits. Rule II: When the two numbers have the same number of digits, we start comparing the digits from left most place until we come across unequal digits. To learn

• ### Standard Form of a Number | Expanded Form | Numeral in Standard Form

We will learn how to write the numeral in standard form. Here the standard form means the process of writing very large expanded form of a number into small form or small number. How to write the number in standard form? Here we will convert expanded form into standard

• ### Expanded Form of a Number | Writing Numbers in Expanded Form | Values

We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its digits. This is shown here: In 2385, the place values of the digits are

• ### Numbers Showing on Spike Abacus | Spike Abacus | Name of a Number

Numbers showing on spike abacus helps the students to understand the number and its place value. Spike abacus is very helpful to understand the concept of magnitude and name of a number.

• ### Numbers from Ten Thousand to One Lakh | 10000 | One Hundred Thousand

We will learn numbers from ten thousand to one lakh. The number 10000 has five digits – the numeral 1 and four zeroes to the right of 1. 10000 stands for ‘0’ ones stands for ‘0’ tens stands for ‘0’ hundreds stands for ‘0’ thousands

• ### Worksheet on Word Problems on Division | Solve Division Problems

In worksheet on word problems on division, all grade students can practice the questions on word problems involving division. This exercise sheet on word problems on division can be practiced by the students to get more ideas to solve division problems.

• ### Worksheet on Estimating Sums and Differences | Find the Estimated Sum

In 4th grade worksheet on estimating sums and differences, all grade students can practice the questions on estimations.This exercise sheet on estimating sums and differences can be practiced

• ### Estimating Sums and Differences | Estimations | Practical Calculations

For estimating sums and differences in the number we use the rounded numbers for estimations to its nearest tens, hundred, and thousand. In many practical calculations, only an approximation is required rather than an exact answer. To do this, numbers are rounded off to a

• ### Worksheet on Mixed Addition and Subtraction | Questions on Addition

In worksheet on mixed addition and subtraction the questions involve both addition and subtraction together; all grade students can practice the questions on addition and subtraction together.

• ### Worksheet on Word Problems on Addition and Subtraction Together | Ans

In 4th grade worksheet on word problems on addition and subtraction, all grade students can practice the questions on word problems based on addition and subtraction. This exercise sheet on

• ### Check for Subtraction and Addition | Checking Subtraction | Problems

We will learn to check for subtraction and addition answers after solving. Difference of two numbers is correct when the sum of the subtrahend number and the difference is equal to the minuend.

• ### Rounding off Numbers | Nearest Multiple of 10 | Nearest Whole Number

Rounding off numbers are discussed here, where we need to round a number. (i) If we purchase anything and its cost is $12 and 23¢, the cost is rounded up to it’s nearest$ 12 and 23¢ is left. (ii) If we purchase another thing and its cost is \$15.78. The cost is rounded up

• ### Money Bills | Prepare a Bill for the Purchases | Copy of an Invoice

We often buy things and then we get money bills of the items. The shopkeeper gives us a bill containing information about what we purchase. Different items purchased by us, their rates and the total

• ### Worksheet on Bills | Bills & Billing of Different Items |Cost of items

We will practice the questions given in the worksheet on bills and billing of different items. We know bill is a slip of paper on which a shopkeeper notes down the requirements of a buyer

• ### Estimating Products | Estimation in Multiplication | Rounding Numbers

To estimate the product, we first round off the multiplier and the multiplicand to the nearest tens, hundreds, or thousands and then multiply the rounded numbers. Estimating products by rounding numbers to the nearest ten, hundred, thousand etc., we know how to estimate