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0. bar(437) expressed in the form
(p)/(q), where
p and
q are integers and
q!=0, is 437

$0 . \overline{437}$ expressed in the form $\frac{p}{q}$ , where $p$ and $q$ are integers and $q \neq 0$ , is $437$

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Transformations of linear functions

Full solution

Q.

0 . \overline{437}

expressed in the form

\frac{p}{q}

, where

p

and

q

are integers and

q \neq 0

, is

437

Assign Variable $x$ : Let $x = 0.\overline{437}$ , which means $x$ is a repeating decimal: $x = 0.437437437\ldots$
Shift Decimal Point: To convert this into a fraction, multiply $x$ by $1000$ to shift the decimal point three places to the right: $1000x = 437.437437\ldots$
Subtract Original $x$ : Now subtract the original $x$ from $1000x$ to get rid of the repeating part: $1000x - x = 437.437437... - 0.437437437...$
Simplify Equation: This simplifies to $999x = 437$ , because the repeating decimals cancel each other out.
Solve for x: Now solve for x by dividing both sides by $999$ : $x = \frac{437}{999}$ .

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