Question

Express 0.2585858.... in p/q form, where p and q are integers and q \mathrel{\char *} 0.​

Answer 1

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Answer 2

SOLUTION

TO DETERMINE

Express 0.2585858.. in p/q form, where p and q are integers and q ≠ 0

EVALUATION

Here the given number is 0.2585858..

Let x = 0.2585858.. - - - - - (1)

Multiplying both sides by 10 we get

10x = 2.585858.. - - - - - - - - (2)

Again Multiplying both sides by 100 we get

1000x = 258.5858.. - - - - - - - -(3)

Equation (3) - Equation (2) gives

990x = 256

$\displaystyle \implies \sf{x = \frac{256}{990} }$

$\displaystyle \implies \sf{x = \frac{128}{495} }$

So the given number in required form is

$\displaystyle \sf{ \frac{128}{495} }$

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