Question

2.034343434..... in p/ q form​

Answer 1

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Here is your answer

$let \: x = 2.0343434343......$

$periodicity = 100$

$100x = 203.43434343.....$

$x = 2.03434343......$

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$99x = 201.40$

$x = \frac{201}{99}$

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Answer 2

$\mathfrak{\large{\underline{\underline{Answer : -}}}}$

$\frac{1007}{495}$

$\mathfrak{\large{\underline{\underline{Explanation : -}}}}$

Let x = 2.0343434...----(1)

Here periodicity = 2

So, multiply the equation by 100

100 * x = 100 * 2.0343434...

100x = 203.3434...---(2)

Subtract (1) from (2)

100x = 203.43434..

-x = 2.03434..

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99x = 201.4

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$x = \frac{201.4}{99}$

$x = \frac{201.4 \times 10}{99 \times 10}$

$x = \frac{2014}{990}$

$x = \frac{2014 \div 2}{990 \div 2}$

$x = \frac{1007}{495}$

Therefore p/q form of 2.03434.. is 1007/495