To solve the given equations, we will break down each calculation step by step.
1. First Equation:
[tex]\[
9.1 \times 10^2
\][/tex]
Here, we are multiplying 9.1 by [tex]\(10^2\)[/tex] (which is 100). When you multiply a number by 100, you essentially move the decimal point two places to the right.
Therefore, the calculation is:
[tex]\[
9.1 \times 100 = 910.0
\][/tex]
So, the first equation is:
[tex]\[
9.1 \times 10^2 = 910.0
\][/tex]
2. Second Equation:
[tex]\[
9.1 \div 10^2
\][/tex]
In this case, we are dividing 9.1 by [tex]\(10^2\)[/tex] (which is 100). When you divide a number by 100, you move the decimal point two places to the left.
Hence, the calculation is:
[tex]\[
9.1 \div 100 = 0.091
\][/tex]
Thus, the second equation is:
[tex]\[
9.1 \div 10^2 = 0.091
\][/tex]
Finally, summarizing both equations:
[tex]\[
9.1 \times 10^2 = 910.0
\][/tex]
[tex]\[
9.1 \div 10^2 = 0.091
\][/tex]
