Question

express 15•712(bar on 12) in p/q form​

Answer 1

$Let \: x = 15.7 \overline {12}$

$\implies x = 15.7121212\cdot\cdot\cdot \:---(1)$

/* Multiply eqution (1) by 10 , we get */

$10x = 157.121212\cdot\cdot\cdot\: ---(2)$

/* Multiply eqution (2) by 100 , we get */

$1000x = 15712.1212\cdot\cdot\cdot\: ---(3)$

/* Subtract eqution (2) from eqution (3), we get */

$\implies 990x = 15555$

$\implies x = \frac{15555}{990}$

$\implies x = \frac{3111}{198}\\= \frac{1037}{66}$

Therefore.,

$\red { 15.7 \overline {12}} \green {=\frac{1037}{66}}$

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