perplexus.info :: Numbers : How many zeros?

How many zeros? (Posted on 2023-07-12)

Given that:

  
  1
------ = 0.000...........0093
 20³⁰           n zeros

Determine the value of n.

Note: Computer program assisted solutions are welcome, but a semi-analytic (simple calculator+p&p) solution is preferred.

*** Adapted from a problem which appeared at the International Mathematics and Science Olympiad in 2020.

See The Solution Submitted by K Sengupta

Rating: 4.0000 (1 votes)

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answer

| Comment 2 of 3 |

Typed into a calculator, 1/20^30 returns 9.31322574615478 x 10^-40.

One of the exponent 40 is used to jump over the digit 9, so 39 zeros are jumped over to get to the decimal point.

Posted by Charlie on 2023-07-12 08:23:46

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