Question

How to write repeating decimals as fractions?

Answer 1

Writing repeating decimals as fractions:

Decimal expansions that do not terminate after a specific number of digits are called repeating or recurring decimals. They have an infinite number of digits after the decimal point. And there is a repetitive pattern in those digits. The steps to convert the repeating decimal to a fraction are:

1. Figure out the recurring digits in the given decimal number.
2. Equate the decimal number with $x$ or any other variable.
3. Identify the number of recurring digits. Let it be $n$. Multiply equation obtained in step $2$ by ${10}^n$. Now you will get another equation.
4. Subtract the equation formed in step $2$ from the equation formed in step $3$.
5. Simplify to get the required answer.

Hence the method to write repeating decimals as fractions are expalined.