2020 AMC 10B Problems/Problem 12
Contents
Problem
The decimal representation ofconsists of a string of zeros after the decimal point, followed by a
and then several more digits. How many zeros are in that initial string of zeros after the decimal point?
Solution
Now we do some estimation. Notice that , which means that
is a little more than
. Multiplying it with
, we get that the denominator is about
. Notice that when we divide
by an
digit number, there are
zeros before the first nonzero digit. This means that when we divide
by the
digit integer
, there are
zeros in the initial string after the decimal point. -PCChess
Video Solution
~IceMatrix
See Also
2020 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.