Sure, let's go through this step-by-step.
1. Write down the numbers we are adding or subtracting:
[tex]\[
\begin{array}{r}
1.230 \\
-8.91 \\
\hline
\end{array}
\][/tex]
2. Align the decimal points and perform the arithmetic operation:
[tex]\[
1.230 + (-8.91) = 1.230 - 8.91
\][/tex]
3. Perform the subtraction:
[tex]\[
1.230 - 8.91 = -7.680
\][/tex]
4. Determine the correct number of significant digits based on the number with the fewest decimal places. Here, [tex]\(1.230\)[/tex] has three decimal places and [tex]\(-8.91\)[/tex] has two decimal places. Our result should be rounded to two decimal places:
[tex]\[
-7.680 \rightarrow -7.68
\][/tex]
5. Lastly, determine the sign of the result. Since [tex]\(-7.68\)[/tex] is less than zero, the result is negative:
[tex]\[
-7.68
\][/tex]
Hence, the final answer, rounded to the correct number of significant digits and including the sign, is:
[tex]\[
-7.68
\][/tex]
Since the answer is negative, we indicate it with a negative sign:
[tex]\[
(-7.68, '-')
\][/tex]
