# What is 5/12 as a decimal?

## Solution

The fraction $$\frac5{12}$$ can be written as $$5\div12$$ .

Carry out the division using the long division method with 5 as the dividend and 12 as the divisor.

As 12 > 5, the division cannot be carried out. Hence place a decimal point in the answer to add 0 to 5.

12 divides 50 four times to give 48.

Subtract 48 from 50 to get the remainder 2.

As 2 is not divisible by 12, add 0 to 2 to get 20. 20 is divisible by 12 one time.
Subtract 12 from 20 to get the remainder 8.

12 divides 80 six times to give 72.
Subtract 72 from 80 to get the remainder 8.

It can be seen that the remainder 8 is repeated as in the previous step.

The repetition of the remainder will give the same digits in the quotient again.

Hence the answer would be 0.4166666….

So 0.4166666…. there is a repeating decimal example.

To denote that the digit 6 is repeating, use a bar above 6 to show that the number is repeated.

$$\frac5{12}=0.41\overline6$$

## Remember

Here are some common terms you should be familiar with.

• In the fraction $$\frac5{12}$$, the number 5 is the dividend (our numerator)
• The number 12 is our divisor (our denominator)

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