Question

express 5.123bar in p/q form where p and q are co primes​

Answer 1

5.123bar in p/q form is $\dfrac{1706}{3\times111}$

where p=1706 and q =3,111 are co primes​

Step-by-step explanation:

Let $\textrm{x}=5.\overline{123}$

$\Rightarrow 10\textrm{x}=51.23\overline{123}$

$\Rightarrow 100\textrm{x}=512.3\overline{123}$

$\Rightarrow 1000\textrm{x}=5123.\overline{123}$

$\Rightarrow 1000\textrm{x}-\textrm{x}=5123.\overline{123}-5.\overline{123}$

$\Rightarrow 999\textrm{x}=5118$

$\Rightarrow \textrm{x}=\dfrac{5118}{999}=\dfrac{1706}{333}=\dfrac{1706}{3\times111}$

Where $\textrm{p}=1706 ,\textrm{q}=3,111$ are co primes