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Maths-

General

Easy

Question

Convert the following repeating decimals to fractions
d) 0.488888888888

hint Hint:

Perform necessary multiplications to make it as a fraction.

The correct answer is: 22/45

Complete step by step solution:
(d) Let x = 0.4888888888
Now multiply by 10 on both the sides,
We get, 10x = 4.888888888
On subtracting from both the sides, we have
$table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 10 x minus x equals 4.88888888 minus 0.48888888 end cell row cell not stretchy rightwards double arrow 9 x equals 4.4 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 4.4 over denominator 9 end fraction end cell end table$
Multiply by 10 on numerator and denominator of x.
On multiplying, we have $22 over 45$ . (Since the numerator and denominator of a fraction must be integers)
On simplification, we get $22 over 45$
Hence 0.4888888 …. = $22 over 45$

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