Problem:
7×539​=
Answer Choices:
A. .7×53.9​
B. .7×.53.9​
C. .7×5.3.9​
D. 7×.53.9​
E. .07×.53.09​
Solution:
To get .9 in the numerator, we must divide it by 10. To maintain equality, we must also divide the denominator by 10. Thus
107×53​109​​=107​×53109​​=.7×53.9​.
In all other cases, the resulting fraction is 101​ or 1001​ of the original fraction.
Answer: A​.
The problems on this page are the property of the MAA's American Mathematics Competitions