To solve the problem of rounding [tex]\( (3.2)^3 \)[/tex] to the nearest tenth, let's go through the steps in detail:
1. Cubing the Value:
First, we need to compute [tex]\( (3.2)^3 \)[/tex]. When [tex]\( 3.2 \)[/tex] is cubed, it is:
[tex]\[
3.2 \times 3.2 \times 3.2 = 3.2^3 = 32.76800000000001
\][/tex]
2. Intermediate Value:
The immediate value from cubing [tex]\( 3.2 \)[/tex] is found to be [tex]\( 32.76800000000001 \)[/tex].
3. Rounding to the Nearest Tenth:
Now, we need to round [tex]\( 32.76800000000001 \)[/tex] to the nearest tenth. When rounding to the nearest tenth, we look at the digit in the hundredths place to decide whether to round the tenths place up or keep it the same:
[tex]\[
\begin{array}{cc}
32.7\underline{6}8 \quad \text{(hundredths place)}
\end{array}
\][/tex]
Since the hundredths place digit (6) is 5 or greater, we round the tenths place up from 7 to 8.
Thus, the rounded value of [tex]\( (3.2)^3 \)[/tex] to the nearest tenth is:
[tex]\[
32.8
\][/tex]
So, the answer is not among the provided options.
However, for the given choices,
30.0 - too low
32.7 - doesn't match the rounded value
Given that the correct rounding leads to an answer that's closer to 32.8, which isn't explicitly listed:
None of the given answers a. 30.0 or b. 32.7 match correctly when rounding accurately.
