How many times is $0.1$ greater than $0.01$?

### Concept & Logic To find out how many times a value $x$ is greater than another value $y$, we evaluate the ratio of the two values by dividing the larger number by the smaller number: $$\text{Multiplier} = \frac{x}{y}$$ ### Step-by-Step Solution * **Given:** The two values are $0.1$ and $0.01$. * **Step 1: Set up the division ratio** $$\text{Ratio} = \frac{0.1}{0.01}$$ * **Step 2: Simplify by eliminating decimals** Multiply both the numerator and the denominator by $100$ to clear the decimal places: $$\frac{0.1 \times 100}{0.01 \times 100} = \frac{10}{1} = 10$$ Hence, $0.1$ is exactly $10$ times greater than $0.01$. ### Exam Strategy & Shortcut Think in terms of shifting the decimal point. To convert $0.01$ into $0.1$, you move the decimal point exactly one spot to the right. Each single-digit shift to the right represents a multiplication by base $10$. Therefore, the answer is $10$ times. ### Common Pitfall Misinterpreting the scale changes in fractional components. A student might quickly glance at the numbers and choose $100$ times because they see two decimal places versus one, confusing the absolute positional step size. ### Final Answer **Therefore, the correct answer is 10 times.**