Simplify the given mathematical expression:
$\frac{9 \times 10^{2}}{9 \times 10^{1}}$

Step 1 ：The given mathematical expression is \(\frac{9 \times 10^{2}}{9 \times 10^{1}}\)

Step 2 ：Both the numerator and the denominator are products of two numbers. The first number in both the numerator and the denominator is 9, and the second number in the numerator is \(10^{2}\), while in the denominator it is \(10^{1}\)

Step 3 ：We can simplify this expression by cancelling out the common factors in the numerator and the denominator. The number 9 is a common factor and can be cancelled out

Step 4 ：The remaining expression is \(\frac{10^{2}}{10^{1}}\). This is a division of two numbers with the same base (10) and different exponents

Step 5 ：According to the laws of exponents, when we divide two numbers with the same base, we subtract the exponent of the denominator from the exponent of the numerator

Step 6 ：So, the simplified expression will be \(10^{2-1}\)

Step 7 ：The simplified expression is 10.0

Step 8 ：Final Answer: The simplified form of the given mathematical expression \(\frac{9 \times 10^{2}}{9 \times 10^{1}}\) is \(\boxed{10}\)