MULTIPLYING DECIMALS BY 10 100 AND 1000

When we multiply decimals, accordingly the number of zeros that we have in 10, 100, 1000…etc. we will move the decimals.

Multiplying a decimal by 10 :

1.3  x 10

Here, we have 10, it has one zero. So we have to move the decimal point to the right of one digit.

Multiplying a decimal by 100 :

3.62  x 100

Here, we have 100, it has two zero. So we have to move the decimal point to the right of two digit.

Multiplying a decimal by 1000 :

56.3  x 1000

Here, we have 1000, it has three zero. So we have to move the decimal point to the right of three digit.

Example 1 :

Find :

a)  38 x 10

b)  9 x 100

c)  3.2 x 10

d)  0.8 x 10

e)  0.71 x 100

f)  2.8 x 100

g)  0.6 x 100

h)  0.83 x 100

i) 1.89 x 10⁴

j)  0.053 x 10³

k) 0.0583 x 1000

l) 0.187 x 100000

Solution :

a)  38 x 10

While multiplying an integer by 10, 100,. ......... etc, we have to add 0 next to it. So, the answer is 380.

b)  9 x 100

Multiplying 9 by 100, we will get 900.

c)  3.2 x 10

• Number of digits we have after the decimal = 1
• Number of zeroes we have in 10 = 1
• Moving the decimal one digit to the right, we get 32.

d)  0.8 x 10

• Number of digits we have after the decimal = 1
• Number of zeroes we have in 10 = 1
• Moving the decimal one digit to the right, we get 8.

e)  0.71 x 100

• Number of digits we have after the decimal = 2
• Number of zeroes we have in 100 = 2
• Moving the decimal two digits to the right, we get 71.

f)  2.8 x 100

• Number of digits we have after the decimal = 1
• Number of zeroes we have in 100 = 2
• Moving the decimal two digits to the right, we add one 0. So, the result is 280.

g)  0.6 x 100

• Number of digits we have after the decimal = 1
• Number of zeroes we have in 100 = 2
• Moving the decimal two digits to the right, we add one 0. So, the result is 60.

h)  0.83 x 100

• Number of digits we have after the decimal = 2
• Number of zeroes we have in 100 = 2
• Moving the decimal two digits to the right. So, the result is 83

i) 1.89 x 10⁴

• Number of digits we have after the decimal = 2
• Number of zeroes we have in 10⁴ = 4
• Moving the decimal four digits to the right, we add two 0's. So, the result is 18900

j)  0.053 x 10³

• Number of digits we have after the decimal = 3
• Number of zeroes we have in 10³ = 3
• Moving the decimal three digits, we get 53.

k) 0.0583 x 1000

• Number of digits we have after the decimal = 4
• Number of zeroes we have in 1000 = 3
• Moving the decimal three digits to the right. So, the answer is 58.3

l) 0.187 x 100000

• Number of digits we have after the decimal = 3
• Number of zeroes we have in 100000 = 5
• Moving the decimal five digits to the right. We have to add two 0's. So, the answer is 18700.

Example 2 :

a)  9.6 ÷ 10 =

b)  16.08 ÷ 10 =

c)  132.22 ÷ 10 =

d)  78.2 ÷ 10 =

e)  9.6 ÷ 100 =

f)  16.08 ÷ 20 =

g) 132.22 ÷ 100 =

h)  78.2 ÷ 20 =

Solution :

a)  9.6 ÷ 10 =

• Number of digits before the decimal = 1
• Number of 0's in 10 = 1
• Moving one digit before the decimal, we get 0.96

b)  16.08 ÷ 10 =

• Number of digits before the decimal = 2
• Number of 0's in 10 = 1
• Moving one digit before the decimal, we get 1.608

c)  132.22 ÷ 10 =

• Number of digits before the decimal = 3
• Number of 0's in 10 = 1
• Moving one digit before the decimal, we get 13.222

d)  78.2 ÷ 10 =

• Number of digits before the decimal = 2
• Number of 0's in 10 = 1
• Moving one digit before the decimal, we get 7.82

e)  9.6 ÷ 100 =

• Number of digits before the decimal = 2
• Number of 0's in 100 = 2
• Moving one digit before the decimal, so we write one 0. We get 0.096

f)  16.08 ÷ 20 =

= 16.08 / (2 x 10)

Dividing 16.08 by 2, we get

= 8.04/10

• Number of digits before the decimal = 1
• Number of 0's in 10 = 1
• Moving one digit before the decimal, we get 0.804

g) 132.22 ÷ 100 =

• Number of digits before the decimal = 3
• Number of 0's in 100 = 2
• Moving one digit before the decimal, we get 1.3222

h)  78.2 ÷ 20 =

= 78.2 / (2 x 10)

Dividing 78.2 by 2, we get

= 39.1/10

• Number of digits before the decimal = 1
• Number of 0's in 10 = 1
• Moving one digit before the decimal, we get 3.91