# What is 2/7 as a decimal?

## Want to practice?

A repeating decimal is a decimal number that has its decimal digits repeated periodically.

For example:

1.83333…., 0.2323232…., 2.254725472547….

Such decimals are represented by placing a bar over the repeating digits.
$$1.8\overline3,\;0.\overline{23},\;2.\overline{2547}$$

## Solution

Let us consider the fraction $$\frac27$$ to be converted to decimal form.
Note that since 2 cannot be divided by 7, you can add zeros to the dividend by placing a decimal point in the quotient.

We get different remainders in each step 6,4,5,1 and 3 after which the remainder is 2. Hence if we were to proceed with the division, we will get the same digits in the quotient again.
The answer would go on as 0.285714285714……

We can stop the division when the remainder repeats itself.

Hence the answer is 0.285714285714……. This is written as $$0.\overline{285714}$$.

## Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac27$$, the number 2 is the dividend (our numerator)
• The number 7 is our divisor (our denominator)

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