Question

Write the decimal representation of $\dfrac{7}{8}$ .

Answer 1

Hint: We will find such a number that gives us such digits in the denominator which are integral powers of $10$ like$10,100,1000,...$ because this will make it easier to do the calculation. So multiply the numerator and denominator with such a number then place the decimal point before the number of digits counting from right to left) the same as the number of zeroes present in the denominator digit.

Complete step-by-step answer:
We have to write the given fraction into a decimal.
Here we will try to make the denominator such a number that it becomes easy for us to do the division. So, if we multiply such a number that the denominator becomes $100$ or $1000$ then it will make the calculation easier for us.
We know that $8 \times 125 = 1000$ so we will multiply the numerator and denominator with $125$. Then we get-
$ \Rightarrow \dfrac{7}{8} \times \dfrac{{25}}{{25}}$
On multiplication, we get-
$ \Rightarrow \dfrac{{875}}{{1000}}$
Now, to convert the given fraction into decimal we will place the decimal point before the number of digits the same as the number of zeroes present in the denominator digit. Since there are three zeroes in the denominator digit so we will place decimal point before three digits of the numerator counting from right to left-
$ \Rightarrow 0.875$
Hence the decimal representation of $\dfrac{7}{8}$ is $0.875$.

Note: Here we can also solve this question by directly dividing the numerator by denominator using the long division method. So we have to divide the numerator by denominator till we get the remainder as zero.
Since we can write $7$ as $7.000$ because the zeroes added after the decimal point do not change the value of the number, then divide the number by $8$. The division is shown below-