Question

What is the value of 9.35 bar

Answer 1

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QUESTION :

We have to put

$\displaystyle \: 9.3 \overline5$

in $\displaystyle \frac{p}{q}$form where p & q are integers with

$\displaystyle \: q \neq \: 0$

CALCULATION :

Let $\displaystyle \: x = 9.3 \overline5$

$\implies \: \displaystyle \:x = 9.35555555......... \: \: \: \: (1)$

Multiplying both sides by 10 we get

$\implies \: \displaystyle \:10x = 93.5555555......... \: \: \: \: (2)$

Multiplying both sides by 10 we get

$\displaystyle \: 100x = 935.5555555........ \: \: \: \: \: (3)$

Now (3) - (2) gives

$\implies \: \displaystyle \:90x = 935 - 93$

$\implies \: \displaystyle \:90x = 842$

$\implies \: \displaystyle \:x = \frac{842}{90}$

$\therefore \: \displaystyle \:x = \frac{421}{45}$

Hence

$\displaystyle \:9.3 \overline5 = \frac{421}{45}$

Answer 2

Answer:

QUESTION :

We have to put

\displaystyle \: 9.3 \overline59.35

in \displaystyle \frac{p}{q}qp form where p & q are integers with

\displaystyle \: q \neq \: 0q=0

CALCULATION :

Let \displaystyle \: x = 9.3 \overline5x=9.35

\implies \: \displaystyle \:x = 9.35555555......... \: \: \: \: (1)⟹x=9.35555555.........(1)

Multiplying both sides by 10 we get

\implies \: \displaystyle \:10x = 93.5555555......... \: \: \: \: (2)⟹10x=93.5555555.........(2)

Multiplying both sides by 10 we get

\displaystyle \: 100x = 935.5555555........ \: \: \: \: \: (3)100x=935.5555555........(3)

Now (3) - (2) gives

\implies \: \displaystyle \:90x = 935 - 93⟹90x=935−93

\implies \: \displaystyle \:90x = 842⟹90x=842

\implies \: \displaystyle \:x = \frac{842}{90}⟹x=90842

\therefore \: \displaystyle \:x = \frac{421}{45}∴x=45421

Hence

\displaystyle \:9.3 \overline5 = \frac{421}{45}9.35=45421