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 = 1 $\text{(B)}$

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1995 AJHSME Problems/Problem 15

Problem

Solution