Mathematik Übungen

# Converting repeating decimals to fractions

## 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. \$0.2\ov57=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:

\$\$3.888\ov8=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=38.888\ov8\$\$

Step 3:
Subtract the number from both sides of the equation. This will help you to get rid off the decimal part:
\$\$10x−x=38.88\ov8−3.88\ov8\$\$

Step 4:
Solve the equation for x:
\$\$9x=35\$\$
\$\$x=35/9\$\$