What is 3/7 as a decimal?

Long Division Method

Fractions are simplified using the long division method. The long division method involves the manual division by dividing the digits one-by-one or pairs until we reach the remainder as zero.

In some divisions, we do not reach the remainder 0 and the division continues repeating the same remainders. In such cases, the quotient will have the decimal number in which one or a particular sequence of numbers occurs again and again. These are called recurring decimal numbers or repeating decimal numbers.

Here the given fraction $$\frac37$$ is a fraction that gives a repeating decimal value.

Let us find the value by dividing the numerator 3 by the denominator 7.

• Note that we have added zeros in each step after placing a decimal point in the quotient.
• In the last step, the remainder is 3, which is the same as the value in the first step. Hence we will get the same digits in the quotient when the division continues.
• Here the digits 428571 are recurring.
• To denote the recurring digits, a bar is placed over them.

Hence the decimal value of the fraction is $$0.\overline{428571}$$.

Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac37$$, the number 3 is the dividend (our numerator)
• The number 7 is our divisor (our denominator)

You may be interested in what is 6/7 as a decimal fraction?