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)

Comments: ( Back to comment list | You must be logged in to post comments.)

In my head solution

Comment 3 of 3 |

20^30 = 2^30*10^30

2^10 is just a bit over 10^3 so 2^30 is just over 10^9

20^30 is just a bit over 10^39

1/20^30 has 39 zeros.

Posted by Jer on 2023-07-12 08:43:29

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