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प्रश्न
Express the following recurring decimal in the form of a rational number `bb(("in fraction form" p/q)`:
`3.2bar(35)`
संख्यात्मक
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उत्तर
Let’s carefully analyse the conversion process to understand how `3203/990` corresponds to `3.2bar(35)`:
1. Let `x = 3.2bar(35)`, that is x = 3.2353535...
2. We note:
Non-repeating part after the decimal = “2” ...(1 digit)
Repeating part = “35” ...(2 digits)
3. Multiply x by 10 to move decimal to right after non-repeating digit:
10x = 32.353535...
4. Multiply (x) by 1000 to move decimal point after one cycle of the repeat:
1000x = 3235.353535...
5. Subtract the equations:
1000x – 10x = 3235.353535... – 32.353535...
1000x – 10x = 3203
990x = 3203
`x = 3203/990`
Hence, the fraction form is `3.2bar(35) = 3203/990`.
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