Problem 5 · 1990 AJHSME
Medium
Fractions, Decimals & Percents
estimation
Which of the following is closest to the product (.48017)(.48017)(.48017)?
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Answer: B — 0.110.
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Hint 1 of 2
The answer choices jump by factors of 10, so you don't need the exact value — you just need the right size. What round, friendly number is .48017 almost exactly equal to?
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Hint 2 of 2
Estimate, don't multiply: replace the messy .48017 with 0.5 (which is 1/2) and cube that. Multiplying out five-decimal numbers would be a waste of time.
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Approach: round to a friendly number, then estimate the size
- The choices (.011, .110, 1.10, 11.0, 110) are spaced a full factor of 10 apart, so the question is really 'how big is it?', not 'what is it exactly.' That means rounding is allowed.
- .48017 is just under 0.5, and 0.5 = 1/2, so the product is about (1/2)×(1/2)×(1/2) = 1/8 = 0.125.
- Of the choices, 0.125 is nearest to 0.110. (The true cube is a touch smaller since .48 < .5, which nudges it down toward .110 — good agreement.)
- *Why this transfers:* when answer choices differ by powers of 10, estimate with the nearest easy number instead of computing — the rounding error is far too small to push you into the wrong bucket.
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