1995 AJHSME Problems/Problem 15

Problem

What is the $100^\text{th}$ digit to the right of the decimal point in the decimal form of $4/37$ ?

$\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 7 \qquad \text{(E)}\ 8$

Solution

$\frac{4}{37}=\frac{12}{111}=\frac{108}{999}=0.108108108...$

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 = $\boxed{\text{(B)}\ 1}$

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
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1995 AJHSME Problems/Problem 15

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