Question

Convert into vulgar fraction

0.1666_ _ _

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Answer 1

First multiply by 10(10−1)=(100−10) to get an integer.

The first multiplier of 10 is to shift the decimal representation one place to the left, so the repeating section begins just after the decimal point. Then the (10−1) multiplier is used to shift the digits one more place to the left (the length of the repeating pattern) and subtract the original to cancel the repeating tail.

(100-10).0.1666=16.666 -1.666 =15

Then divide both ends by (100−10) and simplify:

0.1666=15/100-10 =15/90 =1×15/6×15 =1/6

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