Question

How do you write 0.112 as a fraction?

Answer 1

Hint: In this particular problem, we are given a decimal number having decimal before 3 places. We have to convert this number into a fraction. Fraction consists of numerator and denominator. When we need to remove the decimal, we will add the zeros in the denominator followed by 1. These are the easiest conversions which can be easily understood.

Complete step by step answer:
Let’s discuss the given question in detail.
We know that decimals are those numbers which represent the fraction and a whole number of a number. For example: In 3.16, 3 is a whole number and 16 is a fractional part. The whole number and the fractional part are separated by the dot(.) symbol. When we remove the decimal, zeros will be added to the denominator followed by 1. The total digits which are placed after the decimal will be counted so that we can place only that many zeros in the denominator. If we remove decimal of 3.16 we will get 100 as a denominator like this: $\dfrac{316}{100}$ 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.
As per question, we have:
$\Rightarrow $0.112
Now, remove the decimal:
$\Rightarrow \dfrac{0112}{1000}$
We can see here that we placed 3 zeros in the denominator because after decimal we had 3 digits in the given question.
$\Rightarrow \dfrac{112}{1000}$
Now, we got the fraction but it has to be reduced first. We will take 2 as their lowest factor:
$\Rightarrow \dfrac{56}{500}$
Reduce again with 2:
$\Rightarrow \dfrac{28}{250}$
It can be reduced again with 2:
$\Rightarrow \dfrac{14}{125}$
It cannot be reduced further now. So this will become the final answer.

Note:
Students should note that always start reducing the fraction with their lowest factor. By default the lowest factor is 2. If both numerator and denominator do not get reduced with 2 then go by 3 and so on. Major mistake is done by putting the zeros in the denominator and forgetting to remove the decimal like this: $\dfrac{0.112}{1000}$. Don’t ever make such mistakes.