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Multiplication of Decimals

Multiplication of a Decimal Number by a Whole Number

To multiply a decimal number with a whole number, ignore the decimal point and multiply them
as whole numbers and put the decimal point in the product thus obtained as many places as in
the given decimal number from the right sides towards the left.
For example, 3125 × 3 = 9375. Therefore, 3.125 × 3 = 9.375

3 decimal 3 decimal
places places
Example 14: Find the product of:

(a) 4.8 × 12 (b) 0.37 × 24
Solution: We have
(a) 48 × 12 = 576

\ 4.8 × 12 = 57.6 [1 decimal place]
(b) 37 × 24 = 888

\ 0.37 × 24 = 8.88 [2 decimal places]
Multiplication of a Decimal Number by Another Decimal Number

To multiply a decimal number with another decimal number, ignore the decimal points in both
numbers and multiply them as whole numbers and put the decimal point in the product thus
obtained as many places as equal to the sum of the decimal places in the given decimal numbers
from right sides towards the left.

For example, 3.28 × 2.21 = 7.2488

2 decimal 2 decimal 4 decimal Quick Check
places places places
Example 15: Find the product of: Find the product of the following decimals
and arrange the products in descending order.
(a) 2.7 × 2.68 (b) 7.01 × 0.05 (a) 3.7 × 3 (b) 4.7 × 1.2 (c) 0.3 × 0.3
Solution: We have
(a) 27 × 268 = 7236
\ 2.7 × 2.68 = 7.236 [1 + 2 = 3 decimal places]
(b) 701 × 5 = 3505

\ 7.01 × 0.05 = 0.3505 [2 + 2 = 4 decimal places]
Multiplication of a decimal by 10, 100, 1000, etc.

To multiply a decimal number with 10, 100 or 1000, etc., the digits in the product are same as in
the given decimal number but the decimal point in the product is shifted to the right by as many
places as there are number of zeroes after 1 in multiplier.
For example:
3.25 × 10 = 3.25 = 32.5
(a) 3.25 × 10 = 32.5 (decimal point is shifted 1 place to the right)
3.25 × 100 = 3.25 = 325.0
(b) 3.25 × 100 = 325.0 (decimal point is shifted 2 places to the right)
3.25 × 1000 = 3.25 = 3250.0
(c) 3.25 × 1000 = 3250.0 (decimal point is shifted 3 places to the right)

45 Fractions and Decimals