Write the number 0-35 in the form p-q- where p and q are integers and q - 0

Let x = 0.35 ⇒ nbsp;x = nbsp;0.353535.... —–(1) Multiply nbsp;both sides of (1) by 100 to get 100x = 35.3535.. ——(2) Subtracting (1) from nbsp;(2), ...

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Standard IX

Mathematics

Introduction to Irrational Numbers

Write the num...

Question

Write the number $0. ¯ ¯¯¯¯ ¯ 35$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$

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Solution

Let $x = 0. ¯ ¯¯¯¯ ¯ 35$

$\Rightarrow x = 0.353535.... - - - - - (1)$

Multiply both sides of (1) by 100

to get 100x = 35.3535.. ------(2)

Subtracting (1) from (2), we get

100x - x = (35.35353 ...) - (0.3535...)

$\Rightarrow$ 99x = 35

$\Rightarrow x = \frac{35}{99} Hence, 0. ¯ ¯¯¯¯ ¯ 35 = \frac{35}{99}$

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Write the number 0.¯¯¯¯¯¯35 in the form pq, where p and q are integers and q≠0

Let x=0.¯¯¯¯¯¯35 ⇒x=0.353535....−−−−−(1) Multiply both sides of (1) by 100 to get 100x = 35.3535.. ------(2) Subtracting (1) from (2), we get 100x - x = (35.35353 ...) - (0.3535...) ⇒ 99x = 35 ⇒x=3599Hence, 0.¯¯¯¯¯¯35=3599

Write the number $0. ¯ ¯¯¯¯ ¯ 35$ in the form $\frac{p}{q}$ , where p and q are integers and $q \neq 0$