Solve Calculations Using Powers of Decimals

When we raise a number that is less than 1 to a given power, the answer is smaller than the original number.

 

Example

Work out (0.02)⁴

 

Answer

We must calculate 0.02 x 0.02 x 0.02 x 0.02

 

We know that 2 x 2 x 2 x 2 = 16

But here we must divide each of the 2s by 100

and therefore we must divide the 16 by 100,000,000.

 

16 ÷ 100,000,000 = 0.00000016

 

So,  0.02⁴ = 0.00000016

 

Similarly,  0.2³ = 0.008 and 0.04³ = 0.000064

 

The easiest way to calculate these tricky problems is to count decimal places.

The rule is that you should always have the same number of decimal places in the answer as in the calculation.

 

So, in 0.2³ we have 0.2 x 0.2 x 0.2 which has a total of three decimal places.

The answer of 0.008 also has three decimal places.

 

In 0.04³ we have 0.04 x 0.04 x 0.04 which has six decimal places.

The answer of 0.000064 also has six decimal places.

 

Let's try some questions now - but don't forget to count those decimal places!

 

Want a bit more help with this before you begin? Why not watch this short video?