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Maths-

General

Easy

Question

Convert the following repeating decimals to fractions
c) 0.2151515151515........

hint Hint:

Perform necessary multiplications to make it as a fraction.

The correct answer is: 71/330

Complete step by step solution:
(c) Let x = 0.215151515…(i)
Now multiply by 10 on both the sides in (i),
We get, 10x = 2.151515
Now multiply by 100 on both the sides in (i),
100x = 21.51515
Now multiply by 1000 on both the sides in (i),
1000x = 215.151515
On subtracting 10x from both the sides, we have
$1000 x minus 10 x equals 215.1515 minus 2.151515$
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 990 x equals 213 end cell row cell not stretchy rightwards double arrow x equals 213 over 990 end cell end table$
On simplification, we have $x equals 71 over 330$
Hence 0.2151515151515....... = $71 over 330$

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