Answer :
To determine the error interval for the number [tex]\( n \)[/tex] rounded to one decimal place, and given the result is 10.3, we need to find the range of values that [tex]\( n \)[/tex] can take before it gets rounded to 10.3.
1. Understanding rounding to 1 decimal place: When a number is rounded to one decimal place, it means that the number has been rounded to the nearest tenth.
2. Determine the interval: To find the bounds of the interval, we need to consider the smallest and largest numbers that would round to 10.3 when expressed to one decimal place.
3. Calculate the lower bound: The smallest number that still rounds up to 10.3 when rounded to one decimal place is 10.25 because any number less than 10.25 would round to 10.2.
4. Calculate the upper bound: The largest number that rounds down to 10.3 when rounded to one decimal place is just less than 10.35 (specifically, it is up to but not including 10.35 since 10.35 would round to 10.4).
Therefore, the lower bound is 10.25, and the upper bound is very close to, but not including, 10.35.
So, the error interval for [tex]\( n \)[/tex] is:
[tex]\[ 10.25 \leq n < 10.35 \][/tex]
1. Understanding rounding to 1 decimal place: When a number is rounded to one decimal place, it means that the number has been rounded to the nearest tenth.
2. Determine the interval: To find the bounds of the interval, we need to consider the smallest and largest numbers that would round to 10.3 when expressed to one decimal place.
3. Calculate the lower bound: The smallest number that still rounds up to 10.3 when rounded to one decimal place is 10.25 because any number less than 10.25 would round to 10.2.
4. Calculate the upper bound: The largest number that rounds down to 10.3 when rounded to one decimal place is just less than 10.35 (specifically, it is up to but not including 10.35 since 10.35 would round to 10.4).
Therefore, the lower bound is 10.25, and the upper bound is very close to, but not including, 10.35.
So, the error interval for [tex]\( n \)[/tex] is:
[tex]\[ 10.25 \leq n < 10.35 \][/tex]
