Let's evaluate each clue step by step.
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Clue 1: When rounded to the nearest whole number, I am 8.
- This means the number must be between 7.5 and 8.5 (inclusive of 8.5 and exclusive of 7.5).
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Clue 2: When rounded to the nearest hundredth, I have a 2 in the hundredths place.
- This means the number must have a decimal form ending in .02, .12, .22, .32, .42, .52, .62, .72, .82, or .92.
Now, let's evaluate each number:
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7.602
- Rounds to 8 (valid).
- Does not end in a digit that gives 2 in the hundredths place (ends in .02 - valid).
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8.852
- Rounds to 9 (invalid).
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7.823
- Rounds to 8 (valid).
- Does not end in a digit that gives 2 in the hundredths place (ends in .23 - invalid).
-
8.915
- Rounds to 9 (invalid).
-
8.019
- Rounds to 8 (valid).
- Does not end in a digit that gives 2 in the hundredths place (ends in .19 - invalid).
-
9.193
- Rounds to 9 (invalid).
-
8.246
- Rounds to 8 (valid).
- Ends in .46 (invalid).
-
9.424
- Rounds to 9 (invalid).
From the analysis above, the only number that fulfills both conditions is 7.602.
So, the correct numbers are:
- 7.602