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.

Submitted by K Sengupta

Rating: 4.0000 (1 votes)

Solution: (Hide)

The respective solutions submitted by Charlie and Jer are reproduced ad verbatim as follows:
Method 1(Charlie's Solution):
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.
Method 2(Jer's Solution):
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.

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

Subject	Author	Date
In my head solution	Jer	2023-07-12 08:43:29
answer	Charlie	2023-07-12 08:23:46
Answer	Larry	2023-07-12 07:29:23

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