Let's solve the given expression step by step:
[tex]\[
\frac{5^3}{6} - 24 + \frac{6}{7}
\][/tex]
1. Calculate [tex]\( \frac{5^3}{6} \)[/tex]:
First, compute the exponentiation [tex]\( 5^3 \)[/tex]:
[tex]\[
5^3 = 5 \times 5 \times 5 = 125
\][/tex]
Now, divide by 6:
[tex]\[
\frac{125}{6} \approx 20.833333333333332
\][/tex]
2. Calculate [tex]\( \frac{6}{7} \)[/tex]:
Simply divide 6 by 7:
[tex]\[
\frac{6}{7} \approx 0.8571428571428571
\][/tex]
3. Plug these values into the original expression:
Substitute the values we've calculated:
[tex]\[
20.833333333333332 - 24 + 0.8571428571428571
\][/tex]
4. Perform the subtraction and addition:
Subtract 24 from 20.833333333333332 first:
[tex]\[
20.833333333333332 - 24 = -3.166666666666668
\][/tex]
Now, add [tex]\( \frac{6}{7} \)[/tex] (approximately 0.8571428571428571):
[tex]\[
-3.166666666666668 + 0.8571428571428571 \approx -2.3095238095238106
\][/tex]
5. Round the result to the hundredth:
To round -2.3095238095238106 to the nearest hundredth:
[tex]\[
-2.31
\][/tex]
Therefore, the final rounded value of the given expression to the hundredth place is:
[tex]\[
-2.31
\][/tex]
