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(c) 1 5 3 4 1 • 5 3 4
× 1 7 6 × 1 7 6
9 2 0 4 Multiplication by 6 2 6 9 • 9 8 4
1 0 7 3 8 0 Multiplication by 70 Three decimal
+ 1 5 3 4 0 0 Multiplication by 100 places
2 6 9 9 8 4

Thus, 1.534 × 176 = 269.984

multiplication of Decimals by 10, 100 and 1000

Š When we multiply a decimal number by 10, the decimal point in the product moves
towards the right by one place.

example: (a) 0.73 × 10 = 7.3 (b) 62.40 × 10 = 624.0 = 624

(c) 58.623 × 10 = 586.23 (d) 25.8 × 10 = 258.0 = 258

Š When we multiply a decimal number by 100, the decimal point in the product moves
towards right by two places.
example: (a) 65.432 × 100 = 6543.2 (b) 91.46 × 100 = 9146.0

(c) 0.84 × 100 = 84.0

Š When we multiply a decimal number by 1000, the decimal point in the product moves
towards the right by three places.
example: (a) 0.84 × 1000 = 840.0 = 840 (b) 21.108 × 1000 = 21108.0 = 21108

multiplication of a Decimal by a Decimal

When a decimal number is multiplied by another decimal number, multiply the decimals
as whole numbers by ignoring the decimal points.
Put the decimal point in the product thus obtained after as many places as equal to the

sum of the decimal places in the given decimal numbers.
example 2: Multiply 24.36 by 4.2.
Solution: Step 1: Multiply the two given decimal numbers as we multiply 2 4 3 6
two whole numbers. × 4 2

Step 2: Count the number of decimal places in the given 4 8 7 2
9 7 4 4 0
numbers. In 24.36, number of decimal places = 2. + 1 0 2 3 1 2

In 4.2, number of decimal places = 1.
So, total number of decimal places = 2 + 1 = 3.
Step 3: Count from the right so that the number
of decimal places in the product is equal 24.36 × 4.2 = 102.312

to the sum of decimal places in the given
decimal numbers and put the decimal 2 decimal 1 decimal 3 decimal
place
places
places
point. Thus, 24.36 × 4.2 = 102.312.
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