To solve the given expression:
[tex]\[ \frac{(6.5 - 6.36)}{4.76} \][/tex]
we need to follow these steps:
1. Perform the subtraction in the numerator:
[tex]\[ 6.5 - 6.36 = 0.14 \][/tex]
Here, we subtract 6.36 from 6.5. Both these numbers are given with significant figures (6.5 has 2 significant figures, and 6.36 has 3 significant figures). The result (0.14) has 2 significant figures because in subtraction we keep the significant number based on the least precise decimal place, which is to the nearest hundredths.
2. Set up the expression for division:
[tex]\[ \frac{0.14}{4.76} \][/tex]
3. Perform the division:
[tex]\[ 0.14 \div 4.76 = 0.029411764705882353 \ldots \][/tex]
The exact result of the division is a long decimal number.
4. Determine the number of significant figures for the final answer:
In our problem, the numerator 0.14 has 2 significant figures and the denominator 4.76 has 3 significant figures. When dividing, the result should be rounded to the smaller number of significant figures from the given values, which is 2.
5. Round the result to 2 significant figures:
[tex]\( 0.029 \)[/tex] rounded to 2 significant figures is [tex]\( 0.03 \)[/tex].
Therefore, the final answer with the correct significant figures is:
[tex]\[ \boxed{0.03} \][/tex]
