How do you convert $0.7777$ as a fraction?

Hint: Here we need to write the given decimal in the fractional form. For that, we will first write the numerator as the given decimal number and the denominator as 1. Then we will multiply the number the numerator and denominator by the number 10 until we get the numerator as the whole number. Then we will reduce the fraction obtained if it’s reducible and from there, we will get the final fractional form of the given decimal number.

Complete step by step solution:
Here we need to write the given decimal in the fractional form and the given decimal number is $0.7777$.
For that, we will first write the numerator as the given decimal number and the denominator as 1.
We can write it as
$ 0.7777 = \dfrac{{0.7777}}{1}$
We will multiply the number the numerator and denominator by the number 10 until we get the numerator as the whole number.
So we will first multiply the numerator and denominator by 10.
$ \Rightarrow 0.7777 = \dfrac{{0.7777 \times 10}}{{1 \times 10}} = \dfrac{{7.777}}{{10}}$
We can see that the numerator is still in decimal form. So we will again multiply the numerator and denominator by 10.
$ \Rightarrow 0.7777 = \dfrac{{7.777 \times 10}}{{10 \times 10}}$
On multiplying the numbers, we get
$ \Rightarrow 0.7777 = \dfrac{{77.77}}{{100}}$
We can see that the numerator is still in decimal form. So we will again multiply the numerator and denominator by 10.
$ \Rightarrow 0.7777 = \dfrac{{77.77 \times 10}}{{100 \times 10}}$
On multiplying the numbers, we get
$ \Rightarrow 0.7777 = \dfrac{{777.7}}{{1000}}$
We can see that the numerator is still in decimal form. So we will again multiply the numerator and denominator by 10.
$ \Rightarrow 0.7777 = \dfrac{{777.7 \times 10}}{{1000 \times 10}}$
On multiplying the numbers, we get
$ \Rightarrow 0.7777 = \dfrac{{7777}}{{10000}}$
Now, we can see that the obtained fraction cannot be reduced further as there is no common factor in the numerator and denominator.

Hence, the required fractional form of the given decimal number is equal to $\dfrac{{7777}}{{10000}}$.

Note:
Here we have obtained the fractional form of the given decimal number. A decimal number is defined as the number whose fractional part and the whole number part are separated by a dot which is known as the decimal point. Here we have also reduced the obtained fraction which means to eliminate the common factors in the numerator and denominator. If a fraction has 0 in the denominator then the value of the fraction is infinity. There are generally three types of fraction and they are a proper, improper, and mixed fraction.