Multiplying and dividing by powers of 10

​​In a nutshell

When multiplying or dividing by powers of $$10$$​, you will need to move the decimal point and potentially include some extra zeros. If you are multiplying, the decimal point moves towards the right as the number increases in value. If you are dividing, the decimal point moves towards the left as the number decreases in value.

Multiplying by powers of 10

​​Procedure

1. Count the number of zeros the $$10, 100, 1000$$ etc. has.
   
2. Shift the decimal point of the number being multiplied by that many places to the right. If your decimal point reaches the end of the number, it helps to extend the number by writing in extra zeros at the end of the number, as required.
   
3. The answer is the new number with the new location of the decimal point.
   

Example 1

What is $$658.401 \times 10000$$?

$$10000$$ has $$4$$ zeros, hence move the decimal point $$4$$ places to the right. As there are not $$4$$ digits after the decimal point you can write $$658.401$$ as $$658.4010$$.

Shifting the decimal point $$4$$​ places to the right gives $$\underline{6584010}$$.

​

Dividing by powers of 10

Procedure

1. Count the number of zeros the $$10, 100, 1000$$​ etc. has.
   
2. Shift the decimal point of the number being multiplied by that many places to the left. If your decimal point reaches the end of the number, it helps to extend the number by writing in extra zeros at the beginning of the number, as required.
   
3. The answer is the new number with the new location of the decimal point. If necessary, you may need to write a zero ahead of the decimal point.
   

Example 2

What is $$7304.08\div 100000$$?

​$$100000$$ has $$5$$ zeros, hence move the decimal point $$5$$ places to the left. As there are not $$5$$ digits ahead of the decimal point you can write $$7304.08$$ as $$07304.08$$

Shifting the decimal point $$5$$​ places to the left gives $$\underline{0.0730408}$$.

​