Question

How do you convert \[\dfrac{3}{{40}}\] into a decimal and a percent?

Answer 1

Hint: This is the given number is in fraction form. It is having a numerator and denominator. As we need to convert them into percentage we will multiply it with 100. This is because this fraction is a part of the whole so we will find what part it is of 100%. So we will simply multiply it with 100 and simplify the fraction to simplest form. And in order to convert it in decimal we will perform the division as 3 divided by 40.We will also see some other methods to do the same conversion of fraction into percentage.

Complete step-by-step answer:
First given that \[\dfrac{3}{{40}}\] is a fraction. We will convert this in decimal by actually performing the division. Since fraction is nothing but numerator divided by denominator. So
 \[ \Rightarrow \dfrac{3}{{40}} = \dfrac{3}{4} \times \dfrac{1}{{10}}\]
Now we know that \[\dfrac{3}{4} = 0.75\] . so we can write this as ,
 \[ \Rightarrow \dfrac{3}{{40}} = 0.75 \times \dfrac{1}{{10}}\]
Now dividing by 10 is nothing but shifting the decimal point one place to left.
 \[ \Rightarrow \dfrac{3}{{40}} = 0.075\]
This is the decimal form of a given fraction.
Now in order to convert this in percentage we will multiply it by 100.
  \[ \Rightarrow \dfrac{3}{{40}} = 0.075 \times 100 = 7.5\% \]
This is the percentage form.
So, the correct answer is “7.5%”.

Note: Students note that we are doing two conversions here but no need to get confused.
When we convert a fraction into decimal what we do is actually perform the division and when we convert a fraction into percentage we multiply it with 100 directly. Whereas when we convert decimal into percentage (as we have done in the problem above) we just multiply it by 100 only because we have just converted the fraction into decimal that’s it!