Answer :
To determine the error interval for a number \( w \) that is 65 when rounded to the nearest 5, we need to consider the possible range of values \( w \) could have had before rounding.
1. Understanding rounding to the nearest 5:
When a number is rounded to the nearest 5, it means that the number lies within a certain range around the final rounded value. Specifically, a number will be rounded to 65 if it is closer to 65 than to the nearest other multiples of 5, which are 60 and 70 in this case.
2. Determine the boundaries:
- The number 60 is 5 units less than 65.
- The midpoint between 60 and 65 is 62.5. So, any number greater than or equal to 62.5 and less than 65 will round down to 65.
- The number 70 is 5 units more than 65.
- The midpoint between 65 and 70 is 67.5. So, any number less than 67.5 and greater than or equal to 65 will round down to 65.
3. Formulate the error interval:
Combining these observations, we conclude that:
- The smallest number that would round to 65 when rounded to the nearest 5 is 62.5.
- The largest number that would round to 65 when rounded to the nearest 5 is 67.5.
Therefore, the error interval for \( w \) is \([62.5, 67.5]\).
### Error Interval
[tex]\[ \boxed{[62.5, 67.5]} \][/tex]
1. Understanding rounding to the nearest 5:
When a number is rounded to the nearest 5, it means that the number lies within a certain range around the final rounded value. Specifically, a number will be rounded to 65 if it is closer to 65 than to the nearest other multiples of 5, which are 60 and 70 in this case.
2. Determine the boundaries:
- The number 60 is 5 units less than 65.
- The midpoint between 60 and 65 is 62.5. So, any number greater than or equal to 62.5 and less than 65 will round down to 65.
- The number 70 is 5 units more than 65.
- The midpoint between 65 and 70 is 67.5. So, any number less than 67.5 and greater than or equal to 65 will round down to 65.
3. Formulate the error interval:
Combining these observations, we conclude that:
- The smallest number that would round to 65 when rounded to the nearest 5 is 62.5.
- The largest number that would round to 65 when rounded to the nearest 5 is 67.5.
Therefore, the error interval for \( w \) is \([62.5, 67.5]\).
### Error Interval
[tex]\[ \boxed{[62.5, 67.5]} \][/tex]
