AMC 8 1995 Problem 15

AMC8 1995 年第 15 题

余数与同余★★★☆☆

What is the

100^\text{th}

digit to the right of the decimal point in the decimal form of 4/37 ?

4/37 的小数形式中，小数点右边第 100 位数字是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

\displaystyle \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 =

\text{(B)1}

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