# Mathematics: fractions and recurring decimals.

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## Recurring or terminating.

In a recurring g decimal if there's one dot then there's only o e digit repeating if there are two dots then everything from the first dot to the second is repeated.
Terminating decimals come to an end.
1) Fractions where the denominator has prime factors of only 2 or 5 are terminating all other fractions will give recurring decimals.

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## Recurring decimals into fractions

2) Multiply R by as much needed to get it past a decimal place.

2) when it's past the decimal place the original R is still there so we have to minus it.

Put in practise it looks like this.

R= 0.234 recurring

1000r =234.234 recurring

• R

999R = 234

R= 999/234 = 26/111

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## Fractions into recurring decimals

1) find an equivalent fraction with all nines on the bottom.

2) The number of nines on the bottom tells you the number of digits I. The recurring part e.g. 24/99 = 0.24 recurring from 2 and 4. But 24/999 = 0.024 recurring from .0 to .004.

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