perplexus.info :: Numbers : Decimal Specification

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.

Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Solution: (Hide)

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 a repeating pattern of 51 9s and followed by 102 0s
For an explanation, refer to the solution submitted by Charlie in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
No Subject	K Sengupta	2022-08-02 09:56:33
Solution	Larry	2022-06-13 15:00:50
computer solution	Charlie	2022-06-13 09:02:41

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