Question

How do you write $\dfrac{4}{5}$ in decimal?

Answer 1

Hint: We will just perform the long division, keeping 4 as the dividend and 5 as the divisor and thus we will get the quotient by taking decimal and we would have the required answer.

Complete step by step solution:
We are given that we are required to write $\dfrac{4}{5}$ in decimal.
Here, we will perform long division, by keeping 4 as the dividend and 5 as the divisor.
Thus, we will then get the following division picture with us which we are required to solve:-
$ \Rightarrow 5)\overline 4 $
Since, we can clear see that 4 < 5, therefore, we will require to put a decimal after 4 and write a 0, then we will get the following picture with us:-
$ \Rightarrow 5)\overline {4.0} $
Now, we also know that 8 multiplied by 5 gives us 40, so we have the following picture with us:-
           0.8
$ \Rightarrow 5)\overline {4.0} $
           4.0
           $\overline 0 $
Thus, we have the required answer with us as 0.8.

Note:
The students must note that there are two kinds of decimals: terminating and non – terminating.
Here, we had a terminating decimal. Any fraction with denominator which can be written in the multiple of some powers of 2 and 5 always has a terminating decimal.
Here, we had 5 as the denominator.
Now, we have an alternate way to convert the fraction in decimal as well which is given by as follows:-
$ \Rightarrow \dfrac{4}{5} = \dfrac{{4 \times 2}}{{5 \times 2}}$
Now, simplifying the calculations in the numerator and denominator of the above mentioned expression, we will then obtain the following expression with us:-
$ \Rightarrow \dfrac{4}{5} = \dfrac{8}{{10}}$
Now, we can easily simplify the fraction in the right hand side to a decimal. Since there is one zero in 10, therefore, we will have decimal before one digit of 8.
Thus, we have the required answer with us as $\dfrac{4}{5}$ can be written as 0.8.