Question

How do you convert $87.5\mathrm{\%}$ as a fraction and a decimal?

Answer 1

Hint:
Here we need to know that if we are given the term $n\mathrm{\%}$ then it can be denoted in the form of a fraction as ${\displaystyle \frac{n}{100}}$ and now we can convert this fraction into the decimal as we know that when we divide any number with ${10}^n$ we only need to shift the decimal from right to left in the numerator before the $n\text{th}$ term from the right.

Complete step by step solution:
Here we are given the percentage which we need to convert into the fraction and decimal. So let us first convert it into the fraction form. We need to know that when we are given the number with the percent like $n\mathrm{\%}$ we can write it as ${\displaystyle \frac{n}{100}}$ in the fraction as a percentage is calculated always with respect to $100$
So we can write $87.5\mathrm{\%}={\displaystyle \frac{87.5}{100}}$
Now we know that in order to remove this decimal we can multiply the denominator with the same power of $10$ as there are a number of digits after the decimal. So we need to multiply here the denominator with $10$ and we will get the decimal removed as:
$87.5\mathrm{\%}={\displaystyle \frac{87.5}{100}}={\displaystyle \frac{875}{1000}}$
Now we can know that $875\text{ and 1000}$ can be divisible by $25$ as:
$$\begin{gathered} (25)(35)=875 \\ (25)(40)=1000 \end{gathered}$$
So we can cancel it with the common factor and get ${\displaystyle \frac{875}{1000}}={\displaystyle \frac{35}{40}}$
Now here also $35\text{ and 40}$ are divisible by their common factor $5$ and we will get:
${\displaystyle \frac{35}{40}}={\displaystyle \frac{7}{8}}$
So we get the fraction as ${\displaystyle \frac{7}{8}}$
We know that it is equal to ${\displaystyle \frac{875}{1000}}$
Now if we compare ${10}^n$ with the denominator that is $1000={10}^3$ we will get $n=3$
Now we need to shift the decimal in the numerator from the position where it is now towards the left $3$ terms.
Now we know that in the numerator which is $875$ the decimal point is not there but we can insert it and write it as $875.0$ and now we can move the decimal position three times from right to left.
We can write:
$875=875.0$
Now we will get:
${\displaystyle \frac{87.5}{100}}={\displaystyle \frac{875.0}{100}}=0.875$

So we can write $87.5\mathrm{\%}=0.875$ in the decimal form.

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