Maths-
General
Easy
Question
Convert the following repeating decimals to fractions
c) 0.366666666666
Hint:
Perform necessary multiplications to make it as a fraction.
The correct answer is: 11/30
Complete step by step solution:
(c) Let x = 0.3666666
Now multiply by 10 on both the sides,
We get, 10x = 3.666666
On subtracting x 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 3.666666 minus 0.3666666 end cell row cell not stretchy rightwards double arrow 9 x equals 3.3 end cell row cell not stretchy rightwards double arrow x equals fraction numerator 3.3 over denominator 9 end fraction end cell end table](data:image/png;base64,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)
Multiply by 10 on numerator and denominator of x.
On multiplying, we have .
(Since the numerator and denominator of a fraction must be integers)
On simplification, we get ![11 over 30](data:image/png;base64,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)
Hence 0.3666666…. = ![11 over 30](data:image/png;base64,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)
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△ ADB and △ CBD are congruent by HL-congruence postulate.
![](data:image/png;base64,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)
△ ADB and △ CBD are congruent by HL-congruence postulate.
![](data:image/png;base64,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)
Maths-General