By which decimal number should 0.0001 be divided to get 0.01?

Given :

The given number is 0.0001.

To do :

We have to find the decimal number by which 0.0001 be divided to get 0.01.

Solution :

We know that,

$\frac{a^m}{a^n} = a^{m-n}$

Let the number by which 0.0001 be divided to get 0.01 be x.

$0.0001 = 1 \times 10^{-4}$ (There are four digits after the decimal point)

$0.01 = 1 \times 10^{-2}$  (There are two digits after the decimal point)

Therefore,

$\frac{0.0001}{x} = 0.01$

$x = \frac{0.0001}{0.01}$

$x =\frac{1 \times 10^{-4}}{1 \times 10^{-2}}$

$x = 10^{-4-(-2)}$

 

$x = 10^{-4+2}$

$x = 10^{-2}$

 

$x = 0.01$

The required decimal number is 0.01.