Difference between revisions of "2021 AMC 12A Problems/Problem 5"
Pi is 3.14 (talk | contribs) (→Video Solution by Hawk Math) |
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==Video Solution by Hawk Math== | ==Video Solution by Hawk Math== | ||
https://www.youtube.com/watch?v=P5al76DxyHY | https://www.youtube.com/watch?v=P5al76DxyHY | ||
+ | |||
+ | == Video Solution (Using repeating decimal properties) == | ||
+ | https://youtu.be/vQZ13WiL4WU | ||
+ | |||
+ | ~ pi_is_3.14 | ||
==See also== | ==See also== | ||
{{AMC12 box|year=2021|ab=A|num-b=4|num-a=6}} | {{AMC12 box|year=2021|ab=A|num-b=4|num-a=6}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 17:12, 11 February 2021
Contents
Problem
When a student multiplied the number by the repeating decimal
where
and
are digits, he did not notice the notation and just multiplied
times
. Later he found that his answer is
less than the correct answer. What is the
-digit number
Solution
It is known that and
. Let
. We have that
. Solving gives that
so
. ~aop2014
Video Solution by Punxsutawney Phil
https://youtube.com/watch?v=MUHja8TpKGw&t=359s
Video Solution by Hawk Math
https://www.youtube.com/watch?v=P5al76DxyHY
Video Solution (Using repeating decimal properties)
~ pi_is_3.14
See also
2021 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 4 |
Followed by Problem 6 |
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 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.