Question

Convert $0.15$ into fraction.

Answer 1

Hint: In this question we have been given a decimal number which we have to convert into its equivalent fraction format. A number in decimal format has a decimal point which is a dot after the integer value and a fraction is a number composed of two numbers which are in division. We will convert the number into decimal by multiplying and dividing it with the same number such that the decimal points are removed and we gain a fraction which has a numerator and a denominator. We will then simplify the fraction to get the required solution.

Complete step by step answer:
We have the number given to us as:
$\Rightarrow 0.15$
Now in our decimal number there are two places after the decimal and one integer value before the decimal. Since there are two decimal places, we will multiply the number by ${{10}^{2}}$ which is $100$, to remove the decimal and get the entire number in integer form. Now since we are multiplying the number by $100$, we will also divide the number by $100$ so that its value does not get changed.
On multiplying and dividing by $100$, we get:
$\Rightarrow 0.15\times \dfrac{100}{100}$
On multiplying the terms, we get:
$\Rightarrow \dfrac{15}{100}$
Now the above fraction can be written as:
$\Rightarrow \dfrac{5\times 3}{5\times 20}$
On cancelling the common term $5$, we get:
$\Rightarrow \dfrac{3}{20}$, which is the required solution.

Note: In this question we had a decimal number which had two digits after the decimal number, for this reason we multiplied and divided it by ${{10}^{2}}$. If there are $3$ digits after the decimal place then the number should be multiplied and divided by ${{10}^{3}}$. As a general rule, if there are $n$ digits after the decimal point, the number should be multiplied and divided by ${{10}^{n}}$.