Select all the correct numbers.

The following clues describe me.

When rounded to the nearest whole number, I am 8.
When rounded to the nearest hundredth, I have a 2 in the hundredths place.
Which of the numbers can I be?
7.602 8.852 7.823 8.915 8.019 9.193 8.246 9.424

3 answers

Let's evaluate each clue step by step.

  1. 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).
  2. 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:

  • 7.602

    • Rounds to 8 (valid).
    • Does not end in a digit that gives 2 in the hundredths place (ends in .02 - valid).
  • 8.852

    • Rounds to 9 (invalid).
  • 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
pick some more answers

Let’s re-evaluate the candidates while looking for numbers that meet both clues more thoroughly.

Re-evaluating each number with both clues:

  1. 7.602

    • Clue 1: Rounds to 8 (valid).
    • Clue 2: Rounds to 7.60 (valid, hundredths place is 0, which does not work).
  2. 8.852

    • Clue 1: Rounds to 9 (invalid).
  3. 7.823

    • Clue 1: Rounds to 8 (valid).
    • Clue 2: Rounds to 7.82 (valid, hundredths place is 2, which works).
  4. 8.915

    • Clue 1: Rounds to 9 (invalid).
  5. 8.019

    • Clue 1: Rounds to 8 (valid).
    • Clue 2: Rounds to 8.02 (valid, hundredths place is 2, which works).
  6. 9.193

    • Clue 1: Rounds to 9 (invalid).
  7. 8.246

    • Clue 1: Rounds to 8 (valid).
    • Clue 2: Rounds to 8.25 (valid, hundredths place is 4, which does not work).
  8. 9.424

    • Clue 1: Rounds to 9 (invalid).

Summary of Valid Numbers:

  • 7.602 rounds to 8 but does not satisfy the second clue.
  • 7.823 rounds to 8 and has a 2 in the hundredths place (valid).
  • 8.019 rounds to 8 and has a 2 in the hundredths place (valid).

Thus, the valid numbers that meet both criteria are:

  • 7.823
  • 8.019

Conclusion:

The numbers I can be are 7.823 and 8.019 along with 7.602 from the first answer. The final answers are:

  • 7.823
  • 8.019

Let me know if you have any other queries!