Maths-
General
Easy
Question
Convert the following repeating decimals to fractions
b) 1.5555555555555
Hint:
Perform necessary multiplications to make it as a fraction.
The correct answer is: 14/6
Complete step by step solution:
(b) Let x = 0.55555555
Now multiply by 10 on both the sides,
We get, 10x = 5.5555555
On subtracting x from both the sides, we have
![table attributes columnspacing 1em end attributes row cell 10 x minus x equals 5.55555555 minus 0.555555555 end cell row cell not stretchy rightwards double arrow 9 x equals 5 end cell row cell not stretchy rightwards double arrow x equals 5 over 9 end cell end table](data:image/png;base64,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)
Now we have a fraction for 0.5555555. On adding it with 1, we have
![not stretchy rightwards double arrow 1 plus 5 over 9](data:image/png;base64,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)
as fraction
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