Question 86
Archimedes knew well that $\pi \approx 3.1416$ can be approximated from above by the fraction $22 / 7 \approx 3.1429$ and that at least the first two digits after the decimal point are correct.
For how many pairs of integers $(m, n)$, with $1\lt n\lt 100$, does the decimal expansion of the fraction $\frac{m}{n}$ begin exactly with 3.14?
(A) 14
(B) 21
(C) 48
(D) 50
(E) None of the above
For how many pairs of integers $(m, n)$, with $1\lt n\lt 100$, does the decimal expansion of the fraction $\frac{m}{n}$ begin exactly with 3.14?
(A) 14
(B) 21
(C) 48
(D) 50
(E) None of the above