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Expressing Decimals as Rational Numbers

Question

Express the decimals in the from of $\frac{p}{q}$ :
$0. ¯ ¯¯¯¯¯¯ ¯ 621$

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Solution

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Let $y = 0. ¯ ¯¯¯¯¯¯ ¯ 621 . . . . . . . . . . . . . . . (1) 1000 y = 621. ¯ ¯¯¯¯¯¯ ¯ 621 . . . . . . . . . . . . . . . (2)$

Subtracting (1) from (2)
$999 y = 621 \Rightarrow y = \frac{621}{999}$

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