How many 0's ...
Number Theory
Level
3
Starting from the decimal point, how many 0's are present in the decimal presentation of if we write this number to 1 significant figure?
101
100
99
Infinitely many
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1 solution
The original fraction has denominator 10^101, but lets try some lower numbers.
1/10=0.1 (0)
1/100=0.01 (1)
1/1000=0.001 (2)
It looks like the amount of zeros in the denominator of the fraction is the the number of zeros minus 1 in the decimal representation.
There are 101 zeros in 10^101, so the answer is 100 zeros.
This actually isn't a coincidence, see if you can find out why.