Question

Exprees each of the following decimal numbers in p/q form 0.5 bar

Answer 1

$Let \: x = 0.\bar{5} \: --(1)$

/* Multiplying equation (1) by 10, we get */

$\implies 10x = 5.\bar{5} \: --(2)$

/* Subtract equation (1) from equation (2), we get */

$\implies 9x = 5$

$\implies x = \frac{5}{9} \: \blue{ ( \frac{p}{q} \:form )}$

Therefore.

$\red{ 0.\bar{5} } \green { =\frac{5}{9} \: \blue{ ( \frac{p}{q} \:form )}}$

•••♪

Answer 2

p/q = 5/9 .

Solution :-

$\sf \: Let \: R \: = \: 0. \bar{5} - - - - - - - (1)$

=> Multiply by 10 in equation (1) .

$\sf \: 10R = 5.\bar{5}- - - - - - - - - - - (2)$

=> Subtracting equation (1) from (2) .

=> $\sf \: 10R - R = 0. \bar{5} - 5. \bar{5 }</p><p>$

=> 9R = 5

=> R = 5/9 . ( p/q form)

.°. $\sf{0.\bar{5} }$ = 5/9.