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Decimal Specification (Posted on 2022-06-13)

Given that:

              1
N = ----------------------------
    1.00........00100........001
        50 zeros     50 zeros

is a decimal (base ten) rational number.

Describe the pattern after the decimal point in the decimal expansion of N.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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Solution

| Comment 2 of 3 |

If there were zero zeros in a row, then N would be 1/1.11 = 0.9009009009009008

If there was one zero in a row, then N would be 1/1.0101 = 0.99000099000099

So with groups of 50 zeros as above,

N is "0." followed by a repeating pattern of 51 9s then then 102 0s

Posted by Larry on 2022-06-13 15:00:50

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