Select the related number from the given alternatives: 0.02 : 0.002 :: 1/3 : ?

Introduction / Context:
This is a simple analogy question involving numbers. We are given a pair of numbers 0.02 and 0.002 and asked to find what corresponds to 1/3 in the same way. Such questions test pattern recognition, especially recognizing multiplicative relationships between the first pair and then applying that same relationship to the second number.

Given Data / Assumptions:

• First pair: 0.02 and 0.002.
• Second pair: 1/3 and an unknown number.
• We must find the number that stands in the same relationship to 1/3 as 0.002 does to 0.02.

Concept / Approach:
We observe how 0.02 changes to 0.002. The operation is straightforward: 0.002 = 0.02 / 10. Therefore, the relationship appears to be “divide by 10”. To preserve the same relationship, we must divide 1/3 by 10 to find the corresponding number. This uses the concept of proportional transformation between the two pairs.

Step-by-Step Solution:

Verification / Alternative check:
We can check the ratio form: 0.02 : 0.002 = 0.02 / 0.002 = 10. Similarly, 1/3 : (1/30) = (1/3) / (1/30) = (1/3) * (30/1) = 10. Since both pairs have the same ratio 10, the analogy holds correctly.

Why Other Options Are Wrong:

• 0.333 is approximately 1/3, so it does not represent applying the “divide by 10” operation.
• 0.003 is 0.03 / 10, not 1/3 / 10.
• 3 is the reciprocal of 1/3, corresponding to multiply by 9 rather than divide by 10.

Common Pitfalls:
Some students misread the pattern and attempt to multiply instead of divide, or they try to relate decimal places directly without checking the exact numeric operation. Always check the factor between the numbers (in this case, dividing by 10) and then apply the exact same factor to the new term in the analogy.

Final Answer:
The related number is 1/30.