# Multiplication of a Decimal by 10, 100, 1000

The working rule of multiplication of a decimal by 10, 100, 1000, etc... are:

When the multiplier is 10, 100 or 1000, we move the decimal point to the right by as many places as number of zeroes after 1 in the multiplier.

1. To multiply a decimal by 10, move the decimal point in the multiplicant by one place to the right.

For examples:

(i) 834.7 × 10

Here we multiplied the number 834.7 by 10 so we move 1 place to the right.

Or,

834.7 × 10

= (8347/10) × 10

= 8347/1

= 8347

(ii) 73.5 × 10 = 735

(iii) 100.9 × 10 = 1009

2. To multiply a decimal by 100, move the decimal point in the multiplicant by two places to the right.

For examples:

(i) 98.26 × 100

Here we multiplied the number 98.26 by 100 so we move 2 places to the right.

Or,

98.26 × 100

= (9826/100) × 100

= 9826/1

= 9826

(ii) 6.006 × 100 = 600.6

(iii) 0.77 × 100 = 77

3. To multiply a decimal by 1000, move the decimal point in the multiplicant by three places to the right.

For examples:

(i) 793.41 × 1000

Here we multiplied the number 793.41by 1000 so we move 3 places to the right.

Or,

793.41 × 1000

= (79341/100) × 1000

= 79341 × 10

= 793410

(ii) 9.15 × 1000 = 9150

(iii) 0.017 × 1000 = 17

4. To multiply a decimal by 10, 100, 1000, etc. move the decimal point of the multiplicant as many places to the right as there are zeroes in the multiplier.

For examples:

(i) 1854.347 × 10

Here we multiplied the number by 10 so we move 1 place to the right.

(ii) 72.4 × 100

Here there is only one place after the decimal and 100 has two zeros, so we put one zero at the end of the number.

(iii) 887.43 × 1000

Only 2 places are there after the decimal, but 1000 has 3 zeros, so we put one zero at the end of the number.

Note: Remember that in multiplication of a decimal by 10, 100, 1000, etc. the decimal will be moved to the right by as many places as the number of zeroes in the multiplier and when the number of zeros is more than the digits after the decimal number, then extra zeros must be added to the product.

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