Question

How do you write $0.4$ as a fraction?

Answer 1

Hint:
Here we must know that whenever we are given to find the fraction of the decimal term. We need to remove the decimal first by putting in the denominator the value in the power of ten as per required to remove the decimal. Then we need to convert that fraction in the simplest form.

Complete Step by step Solution:
Here we are given to find the fraction of the decimal term which is given as $0.4$
So we know that whenever we are given the term in the form of decimal we can convert it into the fraction by taking that term in the form of the numerator and denominator. In the denominator comes the ${10^n}$ where $n$ is the number of digits that are present after the decimal in the numerator.
For example: If we have the term $100.12$ so we can write it as $\dfrac{{10012}}{{100}}$
Here we have two terms after the decimal in the numerator, so we have put two zeroes with $1$ in the denominator in order to remove the decimal point from the numerator.
So in the similar way we know that in $0.4$ we have one digit after the decimal in the given decimal. So we will write ${10^1} = 10$ in the denominator and the decimal will be removed from the numerator.
So we can write:
$0.4 = \dfrac{4}{{10}}$
Now we need to convert it into the simplest form. Here we know that both $4{\text{ and 10}}$ are divisible by two and hence we can cancel them and we will be getting:
$\dfrac{4}{{10}} = \dfrac{2}{5}$

Hence we get that $\dfrac{2}{5}$ as the fraction form of $0.4$

Note:
Here in these kind of problems, a student can make mistake by leaving the fraction of $0.4$ as $\dfrac{4}{{10}}$ which is also one of the answers but to get proper result we must convert it into the simplest form where both are not divisible by any common factor.