1. The problem is to simplify the expression $10^1 \times 10^{-2}$. 2. We use the rule of exponents that states when multiplying powers with the same base, we add the exponents: $$a^m \times a^n = a^{m+n}$$ 3. Applying this rule to our problem: $$10^1 \times 10^{-2} = 10^{1 + (-2)} = 10^{-1}$$ 4. The expression simplifies to $10^{-1}$. 5. We can rewrite $10^{-1}$ as a fraction: $$10^{-1} = \frac{1}{10^1} = \frac{1}{10}$$ 6. Therefore, the final answer is $\frac{1}{10}$ or 0.1. This means multiplying $10$ by $10^{-2}$ results in one tenth.