Question

Express each of the following in p/q form 0.3 bar

Answer 1

0.3 bar
x=0.3bar
10x=3.3bar
thus
10x-x=3.3bar-0.3bar
9x=3
x=3÷9
x=1/3

Answer 2

Answer:

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Express the following in the $\frac{p}{q}$ form.

(i) $0.{ \bar{3}}$

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Let x = $\sf{0.{ \bar{3}}}$

${ \sf{⇒x = 0.33333.... \: \: \: \: ...(i)}}$

Multiply both sides of (i) by 10.

$\: \: \: \: { \sf{10x = 3.33333.... \: \: \: \: ...(ii)}}$

Subtracting (i) from (ii), we get

$\: \: \: \: { \sf{10x - x = 3.33333... - 0.33333...}}$

$\: \: \: \:{ \sf{9x = 3}}$

${\sf{⇒ x = \frac{ \cancel{3}}{ \cancel{9} }= \frac{1}{3} }}$

${ \sf{∴ 0.{ \bar{3}} = \frac{1}{3} }}$

$\sf{\color{blue}{Hope \: it \: helps...}}$

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