1954 AMC 12 Problem 34

Attempt Problem 34 of the 1954 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 1954 AMC 12 solutions, or check the answer key.

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34.

The fraction

\dfrac13:

equals

0.33333333

is less than

0.33333333

by

\dfrac1{3\cdot10^8}

is less than

0.33333333

by

\dfrac1{3\cdot10^9}

is greater than

0.33333333

by

\dfrac1{3\cdot10^8}

is greater than

0.33333333

by

\dfrac1{3\cdot10^9}

Answer: D

Concepts:decimal fraction place value

Difficulty rating: 1630

Small hint:

Write

0.33333333

as

\frac{33333333}{10^8}

Big hint:

Subtract this terminating decimal from

\frac{1}{3}

using the denominator

3\cdot10^8

Solution:

Exactly,

\begin{gathered} \frac13-\frac{33333333}{10^8}\\ =\frac{10^8-3(33333333)} {3\cdot10^8}\\ =\frac1{3\cdot10^8}. \end{gathered}

Thus

\frac{1}{3}

is greater by the stated amount.

Thus, the correct answer is D.