## Repeating decimals

A **recurring/repeating decimal** is a number whose digits are periodic (repeating its values at regular intervals) and keep repeating forever, e.g. $1/3=0.333333 ...$ The infinitely repeated digit sequence is called the **repetend**. It can be denoted by a horizontal line (a vinculum) or dots above it, e.g. $0.2ov57=0.257575757 ...$

Every repeating or terminating decimal is a rational number since it can be converted to a fraction.

To convert repeating decimal to fraction follow these steps:

**Step 1:**

Set the repeating decimal equal to fraction x:

$$3.888ov8=x$$

**Step 2:**

Move the repeating digit(s)/repetend to the left of the decimal point by multiplying the decimal by 10, 100, 1000 etc.

$$10x=38.888ov8$$

**Step 3:**

Subtract the number from both sides of the equation. This will help you to get rid off the decimal part:

$$10x−x=38.88ov8−3.88ov8$$

**Step 4:**

Solve the equation for x:

$$9x=35$$

$$x=35/9$$