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8η τάξη

Course: 8η τάξη > Ενότητα 1

Μάθημα 1: Repeating decimals

Writing fractions as repeating decimals review

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Review converting fractions to repeating decimals, and then try some practice problems.

Writing fractions as decimals

To convert a fraction to a decimal, we divide the numerator by the denominator.

Example:start fraction, 2, divided by, 5, end fraction

start fraction, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 5, end color #1fab54, end fraction, equals, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 5, end color #1fab54

$\begin{aligned} &~~ \, 0.{4} \\ \greenD5&\overline{\Big)\blueD2{,}0} \phantom{0000000}& \\ &\underline{\, \mbox{-}0}\,\,\,{\!\downarrow}&\\ &\phantom{0}{2\,\,0}& \\ &\underline{\, \mbox{-}2\,\,0}&\\ &\phantom{00}{\,\,0}&\\ \end{aligned}$

start fraction, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 5, end color #1fab54, end fraction, equals, 0, comma, 4

Writing fractions as repeating decimals

However, it does not always work out that nicely.

Sometimes, when we divide the numerator by the denominator, it becomes clear that the digits will keep repeating. In this case, we write the answer as a repeating decimal.

In our answer, we write a bar over the repeating digits to show that they repeat.

Example:start fraction, 4, divided by, 9, end fraction

start fraction, start color #11accd, 4, end color #11accd, divided by, start color #1fab54, 9, end color #1fab54, end fraction, equals, start color #11accd, 4, end color #11accd, divided by, start color #1fab54, 9, end color #1fab54

$\begin{aligned} &~~ \, 0.{4444} \\ \greenD9&\overline{\Big)\blueD4.0000} \phantom{0000000}& \\ &\underline{\, \mbox{-}0}\,\,\,{\!\downarrow}&\\ &\phantom{0}{4\,\,0}& \\ &\underline{\, \mbox{-}3\,\,6}{\,\,\!\downarrow}&&\\ &\phantom{00}{\,\,4\,0}&\\ &\underline{\,\,\,\,\,\, \mbox{-}3\,6}{\,\,\!\downarrow}\,\,\\\ &\phantom{0000}{4\,0}& \\ &\underline{\,\,\,\,\,\,\,\,\,\, \mbox{-}3\,6}&\\ &\phantom{000\,\,0}{\,\,4}&\\ \end{aligned}$

No matter how long we divide, the 4 will continue to repeat in our quotient.

start fraction, start color #11accd, 4, end color #11accd, divided by, start color #1fab54, 9, end color #1fab54, end fraction, equals, 0, point, start overline, 4, end overline

Want to learn more about writing fractions as repeating decimals? Check out this video.

Εξάσκηση

Πρόβλημα 1

Τρέχων

Select the decimal that is equivalent to start fraction, 2, divided by, 3, end fraction.

Want to try more problems like this? Check out this exercise.

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