Year 7 Interactive Maths - Second Edition

Multiplication of a Decimal by a Power of Ten

Recall that:

So, the powers of 10 include numbers such as 10, 100, 1000, 10 000, ….

Consider the multiplication 1.56 ×1000.

To calculate 1.56 ×1000, ignore the decimal point and multiply the digits.  There are 2 decimal places in the number being multiplied.  So, there will be 2 decimal places in the answer.

Note:

The multiplication of 1.56 ×1000 could be obtained by shifting the decimal point to the right in the answer by the number of places equal to the number of zeros in the multiplier, 1000.  That is, a shift of three decimal places.

In general:

If a decimal number is multiplied by a power of 10, then to obtain the answer, simply shift the decimal point to the right in the number being multiplied by the number of places equal to the number of zeros in the multiplier.

Example 15

Calculate 6.84 ×10.

Solution:

Example 16

Calculate 13.468 ×100.

Solution:

Example 17

Calculate 93.28 ×1000.

Solution:

Example 18

Calculate 0.5 ×100.

Solution:

Example 19

Calculate 0.06 ×1000.

Solution:

Example 20

Calculate 0.0035 ×10 000.

Solution: