# 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

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