To determine the difference between the given values to the correct level of precision, we can follow these steps:
1. Identify the Values:
- The first value is [tex]\( 22.108 \, L \)[/tex]
- The second value is [tex]\( 5.80 \, L \)[/tex]
2. Subtract the Second Value from the First:
[tex]\[
22.108 \, L - 5.80 \, L = 16.308 \, L
\][/tex]
Thus, the raw difference between the two values is [tex]\( 16.308 \, L \)[/tex].
3. Determine the Correct Level of Precision:
- The first value, [tex]\( 22.108 \, L \)[/tex], is given to three decimal places.
- The second value, [tex]\( 5.80 \, L \)[/tex], is given to two decimal places.
According to the rules of precision, the result should have the same number of decimal places as the number with the least precision. Here, [tex]\( 5.80 \, L \)[/tex] dictates the precision, which is to two decimal places.
4. Round the Raw Difference to the Correct Precision:
- The raw difference [tex]\( 16.308 \, L \)[/tex] should be rounded to two decimal places.
When rounding [tex]\( 16.308 \, L \)[/tex] to two decimal places, we get:
[tex]\[
16.31 \, L
\][/tex]
Therefore, the correct difference, rounded to two decimal places, is [tex]\( 16.31 \, L \)[/tex].
So, the answer is [tex]\( \boxed{16.31 \, L} \)[/tex].
