QUESTIONS ON 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