Problem: The fraction, 31:
Answer Choices:
A. equals 0.33333333
B. is less than 0.33333333 by 3⋅1081
C. is less than 0.33333333 by 3⋅1091
D. is greater than 0.33333333 by 3⋅1081
E. is greater than 0.33333333 by 3⋅1091
Solution:
1/3 is the infinite repeating decimal 0.333…. Thus 1/3 is greater than 0.33333333 by the amount 0.00000000333⋯=1/3⋅108;
or
0.33333333=3⋅10−1+3⋅10−2+⋯+3⋅10−8=1−10−13⋅10−1(1−10−8)=93(1−10−8)=31−310−8=31−3⋅1081