Comparing two small decimals by division Evaluate: 0.0169 ÷ 0.013 = ?

Introduction / Context: Dividing close decimal values often yields a simple ratio if the numerator is a multiple of the denominator. Recognizing 0.0169 as 1.3 times 0.013 speeds up the solution.

Given Data / Assumptions:

• Compute 0.0169 / 0.013.
• All values are exact decimals.

Concept / Approach: Check whether 0.013 times a simple decimal like 1.3 equals 0.0169. Since 13 * 13 = 169, this becomes a straightforward mental check using scaled integers.

Step-by-Step Solution:Compute 0.013 * 1.3 = (13/1000) * (13/10) = 169/10000 = 0.0169.Therefore 0.0169 / 0.013 = 1.3.

Verification / Alternative check: Express as fractions: (169/10000) / (13/1000) = (169/10000) * (1000/13) = 169/130 = 1.3. Exact match.

Why Other Options Are Wrong:.13 and .013: Both are much less than 1, but the numerator is larger than the denominator, so the result must exceed 1.13: Ten times too large; would imply 0.013 * 13 = 0.169, not 0.0169.

Common Pitfalls: Misplacing decimal points when multiplying 13 by 13; forgetting that quotient > 1 since numerator > denominator. Validate by multiplying back.

Final Answer: 1.3