Find the missing divisor from a decimal ratio Solve for x in: 0.001 / x = 0.01.

Introduction / Context:
Finding an unknown divisor requires rearranging a simple equation. This question also reinforces understanding of decimal magnitudes and how dividing by a small number increases the quotient.

Given Data / Assumptions:

• 0.001 / x = 0.01.
• All numbers are base-10 decimals.

Concept / Approach:
Multiply both sides by x and then divide by 0.01 to isolate x. Alternatively, express decimals as powers of 10 to visualize the scaling factor clearly.

Step-by-Step Solution:
0.001 / x = 0.01 ⇒ 0.001 = 0.01 * x.Solve for x: x = 0.001 / 0.01.Compute: 0.001 / 0.01 = 0.1.

Verification / Alternative check:
Using powers of 10, 0.001 = 10^-3 and 0.01 = 10^-2, so x = 10^-3 / 10^-2 = 10^(-3+2) = 10^-1 = 0.1. Substitution check: 0.001 / 0.1 = 0.01. Correct.

Why Other Options Are Wrong:
10: Would give 0.001 / 10 = 0.0001, not 0.01..01 or .001: These produce 0.1 or 1 in the quotient, not 0.01.

Common Pitfalls:
Inverting incorrectly (taking x = 0.01 / 0.001). Keep the equation order intact and isolate x systematically.

Final Answer:
0.1