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Year 7 Interactive Maths - Second Edition


Multiplication of a Decimal by a Power of Ten

Recall that:

Powers of ten
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 that there are 2 decimal places in the number being multiplied and so there are 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:

Move the decimal point 1 place to the right.


Example 16

Calculate 13.468 100.

Solution:

Move the decimal point 2 places to the right.


Example 17

Calculate 93.28 1000.

Solution:

Move the decimal point 3 places to the right.


Example 18

Calculate 0.5 100.

Solution:

Move the decimal point 2 places to the right.


Example 19

Calculate 0.06 1000.

Solution:

Move the decimal point 3 places to the right.


Example 20

Calculate 0.0035 10 000.

Solution:

Move the decimal point 4 places to the right.


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