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प्रश्न
Express the following recurring decimal in the form of a rational number `bb(("in fraction form" p/q)`:
`0.bar(6)`
संख्यात्मक
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उत्तर
The recurring decimal `0.bar(6)` which means 0.6666... repeating can be expressed as a fraction in the following way:
Let `x = 0.bar(6)`.
Multiply both sides by 10 since the repeating part is one digit:
10x = 6.6666...
Now subtract the original x = 0.6666... from this:
10x – x = 6.6666... – 0.6666...
9x = 6
`x = 6/9`
`x = 2/3`
Therefore, `0.bar(6) = 2/3`.
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