Question

Write 0.125 as both percent and a fraction.
$$\begin{gathered} A.1.25\mathrm{\%}and{\displaystyle \frac{1}{4}} \\ B.12.5\mathrm{\%}and{\displaystyle \frac{1}{8}} \\ C.125\mathrm{\%}and{\displaystyle \frac{2}{9}} \\ D.0.125\mathrm{\%}and{\displaystyle \frac{1}{5}} \end{gathered}$$

Answer 1

Hint:- First we had to simply divide the number by $${10}^x$$, where x will be the number of digits on the right side of the decimal point and then remove the decimal from numerator to change the given number in fraction form and then to find the percentage of that we simply multiply that by 100.

Complete step-by-step solution -
Let us find the fraction form of the number 0.125.
So, to change the decimal number to fractional number we had to divide the decimal number by $${10}^x$$, where x is the number of digits after the decimal point and remove the decimal point from the numerator.
So, there are three digits after decimal point in the number 0.125
So, dividing 0.125 by $${10}^3$$ and then removing the decimal point from the numerator. We get the fractional number as $${\displaystyle \frac{125}{1000}}$$ but we had to reduce this number to the lowest fractional number. So for that we divide the numerator and denominator by common factors.
$$\Rightarrow$$ fraction of 0.125 will be $${\displaystyle \frac{125}{1000}}={\displaystyle \frac{25}{200}}={\displaystyle \frac{5}{40}}={\displaystyle \frac{1}{8}}$$
So, the fraction of 0.125 will be $${\displaystyle \frac{1}{8}}$$
To find the percent of 0.125 we had to multiply its fraction by 100.
$$\Rightarrow$$ Percent of 0.125 will be $${\displaystyle \frac{1}{8}}\times 100={\displaystyle \frac{100}{8}}={\displaystyle \frac{50}{4}}={\displaystyle \frac{25}{2}}=12.5\mathrm{\%}$$
So, the percentage of 0.125 is 12.5% and the fraction is $${\displaystyle \frac{1}{8}}$$.
Hence, the correct option will be B.

Note:- Whenever we come up with this type of problem then if we are only asked to find the percent then there is no need to change the fraction to its lowest form because the percent will remain the same. Like the percent of $${\displaystyle \frac{125}{1000}}$$ and $${\displaystyle \frac{1}{8}}$$ is the same. i.e. $${\displaystyle \frac{125}{1000}}\times 100={\displaystyle \frac{1}{8}}\times 100=12.5\mathrm{\%}$$. This will be the easiest and efficient way to find the solution of the problem.