Question

How do you convert $\dfrac{9}{{100}}$ into a decimal and percent?

Answer 1

Hint: Here we know that when we divide any number with ${10^n}$ we only need to shift the decimal form right to left in the numerator till the $n{\text{th}}$ term from the right and when we multiply that fraction by $100$ we get the percentage required.

Complete step by step solution:
Here we are given the fraction $\dfrac{9}{{100}}$ which we need to convert into the decimal first and then into the percentage. So we know that when we divide any number with ${10^n}$ we only need to shift the decimal form right to left in the numerator till the $n{\text{th}}$ term from the right and when we multiply that fraction by $100$ we get the percentage required. An example can make it clearer.
For example: If we have $\dfrac{4}{{10}}$ as the fraction and we can compare the denominator with ${10^n}$so we get that $n = 1$ and therefore we need to move in numerator from right to left till $n{\text{th}}$ term and then put decimal over there. So here when we move from right to left in the numerator which is \[4\] one time and we get the result as $0.4$.
Now we need to see the fraction we are given:
We are given the $\dfrac{9}{{100}}$ and therefore if we now compare the denominator now with ${10^n}$so we get that $n = 2$ and therefore we need to move in numerator from right to left till $n{\text{th}}$ term and then put decimal over there. So here when we move from right to left in the numerator which is \[9\] two times and we get the result as $0.09$
So the decimal form of the fraction $\dfrac{9}{{100}}$ is $0.09$
Now we need to convert this fraction into the percent. We must know that whenever we are given to convert any fraction into a percentage we just need to multiply that fraction with $100$ and hence we will get:

Percent$ = \dfrac{9}{{100}} \times 100 = 9\% $

Note:
Here the student must remember that whenever we need to convert a fraction with the denominator as ${10^n}$where $n \in Z,n > 0$ we just need to shift the decimal in the numerator from right to left till $n$ terms.