Question

How do you convert 3.12 into a fraction and percent?

Answer 1

Hint: Here in this question, we are given a number in decimals and we have to convert it into the fraction by removing the decimal. Further we also have to convert it into the percent. To convert into percent, the fraction we obtain will be multiplied by 100%. Additionally the obtained fraction has to be reduced into simplest form.

Complete step by step answer:
Let’s solve the question now.
As we all know that decimal are the numbers which represent the fractional part of a number. For example in 2.16, 2 is a whole number and 16 is a fractional part. The whole number and the fractional part are separated by the dot(.). When we remove the decimal, 1 will be placed in the denominator followed by the number of zeros as per the number of digits after the decimal. If we remove decimal of 2.16 we will get 100 as a denominator like this: $\dfrac{216}{100}$ because after decimal there are 2 digits i.e. 1 and 6 so we will place 2 zeros after 1 in denominator. After this conversion, when we obtain a fraction, it can also be reduced to lowest terms. And as per question they have also asked to convert the decimal into percent. Percent (%) represents the fraction of 100. Now let’s see how!
First, remove the decimal of 3.12 and place the zeros in its denominator.
$\Rightarrow \dfrac{312}{100}$
Now, we got the fraction from a decimal. Now, it is getting reduced. So reduce it until we find the simplest form of it. Let’s start with 2:
$\Rightarrow \dfrac{156}{50}$
On reducing further with 2, we will get:
$\Rightarrow \dfrac{78}{25}$
And now, it can’t be reduced more. So the final step is to find the percent. Previously we obtained the fraction:
$\Rightarrow \dfrac{312}{100}$
In this, the 100 will change into % sign and forms the percentage as 312%.

Note: You need to remember that when we convert a decimal into percent, first it is converted to fraction and automatically the denominator forms the percent as % is equal to 100. Always represent the fraction in simplest form. But for percent, we have to just remove decimal and convert to fraction. Simplest form is not required there.