1988 AMC 8 Problem 8

Attempt Problem 8 of the 1988 AMC 8 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 1988 AMC 8 solutions, or check the answer key.

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

8.

Betty used a calculator to find the product 0.075×2.56.0.075 \times 2.56. She forgot to enter the decimal points. The calculator showed 19200.19200. If Betty had entered the decimal points correctly, the answer would have been
0.01920.0192
0.1920.192
1.921.92
19.219.2
192192
Answer: B
Concepts:decimalplace value
Small hint:
Count the total number of decimal places in 0.0750.075 and 2.562.56
Big hint:
There are 3+2=53 + 2 = 5 decimal places, so place the decimal point that many digits from the right of 1920019200
Solution:
The factors 0.0750.075 and 2.562.56 have 33 and 22 decimal places, for a total of 5.5.
Placing the decimal point 55 digits from the right of 1920019200 gives 0.19200=0.192.0.19200 = 0.192.
Thus, the correct answer is B .
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