Problem 12 · 1988 AJHSME
Hard
Fractions, Decimals & Percents
cancel-powers-of-ten
Suppose the estimated 20 billion dollar cost to send a person to the planet Mars is shared equally by the 250 million people in the U.S. Then each person's share is
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Answer: C — 80 dollars.
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Hint 1 of 2
Don't write out all those zeros. Measure both amounts in the same unit — 'millions' — so the giant word on each side cancels. How many millions is 20 billion?
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Hint 2 of 2
A billion is 1000 millions, so 20 billion = 20,000 million. Now both top and bottom are 'so-many million,' and the 'million' cancels.
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Approach: rewrite both numbers in the same unit, then cancel it
- Put both amounts in millions: 20 billion = 20,000 million, and the population is 250 million. Now the shared word 'million' cancels top and bottom: 20,000 million ⁄ 250 million = 20,000 ⁄ 250.
- 20,000 ⁄ 250 = 80 dollars.
- Why this transfers: when a quotient mixes huge words like billion and million, convert both to the same scale so that scale cancels. You're left dividing small, friendly numbers instead of juggling rows of zeros.
Mark:
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