Question

Convert in p/q form 0.0123 ( bar on 23 )

==Full procedure needed==

Answer 1

Hola Mate!!

Your answer :-

$= > 0.0123232323...... \\ \\ let \: x = 0.0123232323...... \\ \\ = > 100x = 001.23232323......(a) \\ \\ = > 10000x = 00123.23232323......(b) \\ \\ subtract(a)and(b) \\ \\ = > 10000x - 100x = 00123.232323... - 001.232323... \\ \\ = > 9900x = 122 \\ \\ = > x = \frac{122}{9900} \\ \\ = > x = \frac{61}{4950}$

☆ Hope it helps ☆

Answer 2

Let x = 0.01$\bar{23}$

Reducing all extra terms after decimal except bar number, { to reduce , multiply by 100 on both sides }

100 x = 1.$\bar{23}$

Now, As there are two numbers under bar, multiply by 100 on both sides,

10000 x = 123.$\bar{23}$

Then, subtract 100x from both sides,

10000 x = 123.$\bar{23}$

-100 x = 1.$\bar{23}$

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9900 x = 122 [ bar numbers will be cancel }

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$\rightarrow x = \frac{122}{9900}$

Hence,

0.01$\bar{23} = \frac{122}{9900}$