Sure! Let's determine the possible values for a three-digit number composed of the digits 3, 5, and 6, that rounds to 700 when rounded to the nearest hundred. To do this, we need to investigate the rounding rules and apply them step-by-step.
First, let's consider what it means for a number to round to 700 when rounded to the nearest hundred.
When rounding a number to the nearest hundred:
- The key digit to examine is the tens digit.
- If the tens digit is 5 or higher, the hundreds digit rounds up.
- If the tens digit is lower than 5, the hundreds digit remains the same.
We are given that our number consists of the digits 3, 5, and 6. We need to use these digits in such a way that the resulting number rounds to 700.
For a number to round up to 700, its hundreds digit must be 6 (not yet rounded), as any number with hundreds digit 6 and any suitable tens and ones digits will round up to the next hundred, which is 700.
Next, let's determine the range of numbers between 650 (the lowest possible number to round to 700) and 699:
- The lowest number in this range is 650.
- The highest number in this range is 699.
Hence, the three-digit number composed of 3, 5, and 6, which rounds to 700, must fall within 650 to 699:
- > Evaluate Possible Numbers:
- If the hundreds digit is 6 (as concluded above):
- 635 (but 3 is less than 5, can't round up to 700)
- 653 (5 is valid but should be paired with tens or ones to make it rounding up to 700)
- ...
...
Given the digits 3, 5, and 6, and the range we derived, let's combine:
- Numbers in range of 350 to 399 that utilize the digits ensuring accurate rounding to hundred gives:
- Example evaluation:
- 356 (digit 5 valid, rounds up to 400)
- If apply similar approach:
...
Finally, based on this evaluation ensuring digits used correctly defining range compliance, the answered derived can be stated as:
Thus, the correct three-digit number comprising of 3, 5, and 6 which rounds to 700 when rounded to the nearest hundred must be a number between 650 and 699.
Thus, the correct number falls in this range [650, 699]:
Summary:
Possible number combinations of desired resolution considering rounding:
Can conclude result.
