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Converting repeating decimals to fractions

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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:
$$9x=35$$
$$x=35/9$$


   
   

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