Question

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

Answer 1

pick some more answers

Answer 2

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**

Answer 3

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!