Problem 4 · 2017 AMC 8
Easy
Arithmetic & Operations
estimate-and-pick
When 0.000315 is multiplied by 7,928,564 the product is closest to which of the following?
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Answer: D — 2400.
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Hint 1 of 2
The answer choices jump by powers of 10 (210, 2100, 24000…), so you don't need a precise product — you only need the right size. Round each number to one digit.
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Hint 2 of 2
Separate the problem into two easy parts: multiply the leading digits (3 × 8), and separately track the powers of 10. That's the heart of scientific-notation estimation.
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Approach: estimate via scientific notation
- Round to one significant figure: 0.000315 ≈ 3 × 10−4, and 7,928,564 ≈ 8 × 106. The choices are spread by factors of 10, so this rounding is safe.
- Multiply the fronts and add the exponents: (3 × 8) × 10−4 + 6 = 24 × 102 = 2400.
- Why this transfers: whenever answer choices differ by orders of magnitude, estimate — nail the leading digit and the exponent, and ignore the rest.
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