# What is 5/9 as a decimal? ## Want to practice?

### Solution

A repeating decimal fraction is a fraction that, when divided, gives a decimal in which a digit or a sequence of digits repeats itself in a pattern.

The digits that are repeated are after the decimal point. We use the long division method to find if a fraction gives a repeating decimal as an answer.

The long division is done with the numerator as the dividend and the denominator as the divisor. Here the numerator 5 is the dividend and the denominator 9 is the divisor. Note that we add a 0 to 5 to make it divisible by 9.

The number 50 is divisible by 9 five times giving 45. We get 5 as the remainder in the first step.

In the second step, we have 50 again, which is divisible 5 times by 9 giving 5 as a reminder again.

We can conclude that the same remainder will be the result of further division. Hence here the digit 5 in the quotient is the repeating number and is infinite.

The answer to the fraction $$\frac{\mathbf5}{\mathbf9}$$ is 0.555……

The repeating decimals can be written in a terminating form by placing a bar over the digit that is repeated

$$\mathbf0\boldsymbol.\mathbf{555}\boldsymbol.\boldsymbol.\boldsymbol.\boldsymbol=\mathbf0\boldsymbol.\overset{\boldsymbol¯}{\mathbf5}$$

## Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac{5}{9}$$, the number 5 is the dividend (our numerator)
• The number 9 is our divisor (our denominator)

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