Difference between revisions of "1995 AJHSME Problems/Problem 15"
Mrdavid445 (talk | contribs) (Created page with "==Problem== What is the <math>100^\text{th}</math> digit to the right of the decimal point in the decimal form of <math>4/37</math>? <math>\text{(A)}\ 0 \qquad \text{(B)}\ 1 \q...") |
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<math>\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8</math> | <math>\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8</math> | ||
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| + | ==Solution== | ||
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| + | <math>\frac{4}{37}=\frac{12}{111}=\frac{108}{999}=0.108108108...</math> | ||
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| + | Since this repeats every three digits, digit number x = digit number (x mod 3), and the 100th digit = (100 mod 3)th digit = 1st digit = <math>\boxed{\text{(B)}\ 1}</math> | ||
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| + | |||
| + | ==See Also== | ||
| + | {{AJHSME box|year=1995|num-b=14|num-a=16}} | ||
| + | {{MAA Notice}} | ||
Latest revision as of 00:23, 5 July 2013
Problem
What is the 
digit to the right of the decimal point in the decimal form of 
?
Solution
Since this repeats every three digits, digit number x = digit number (x mod 3), and the 100th digit = (100 mod 3)th digit = 1st digit = 
See Also
| 1995 AJHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 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 AJHSME/AMC 8 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
