Comparing the numbers 10^-49 and 2×10^-50, we may say:

(C) the first exceeds the second by 8×10^-50

(A) the first exceeds the second by 8×10^-1

(B) the first exceeds the second by 2×10^-1

(D) the second is five times the first

(E) the first exceeds the second by 5

1957 AMC 12 Problem 12

Attempt Problem 12 of the 1957 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1957 AMC 12 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

12.

Comparing the numbers

10^{-49}

and

2\cdot10^{-50},

we may say:

the first exceeds the second by

8\cdot10^{-1}

the first exceeds the second by

2\cdot10^{-1}

the first exceeds the second by

8\cdot10^{-50}

the second is five times the first

the first exceeds the second by

5

Express both numbers with the same power of ten

Rewrite

10^{-49}

10\cdot10^{-50}

Using a common power of ten,

\begin{gathered} 10^{-49}-2\cdot10^{-50}\\ =(10-2)10^{-50}\\ =8\cdot10^{-50}. \end{gathered}

Thus, the correct answer is C.