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 = 1 \text{(B)} | ||
Revision as of 12:54, 5 July 2012
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 = 1 \text{(B)}
