Problem:
What is the minimum number of digits to the right of the decimal point needed to express the fraction 226⋅54123456789​ as a decimal?
Answer Choices:
A. 4
B. 22
C. 26
D. 30
E. 104
Solution:
The numerator and denominator of this fraction have no common factors. To express the fraction as a decimal requires rewriting it with a power of 10 as the denominator. The smallest denominator that permits this is 1026 :
226⋅54123456789​=226⋅54⋅522123456789⋅522​=1026123456789⋅522​
so the numeral will have 26​ places after the decimal point. In fact
226⋅54123456789​=0.00294343922138214111328125
The problems on this page are the property of the MAA's American Mathematics Competitions