Question

Column A: \(\frac{0.27}{0.53}\)
Column B: \(\frac{0.027}{0.053}\)

• A. The quantity in Column A is greater.
• B. The quantity in Column B is greater.
• C. The two quantities are equal.
• D. The relationship cannot be determined from the information given.

Hint:

When comparing fractions with decimals, look for proportionality. Notice that the numerator in Column B (0.027) is the numerator of Column A (0.27) divided by 10. The same is true for the denominators (0.053 vs 0.53). Since both parts of the fraction were changed by the same factor, the fractions are equal.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
This question tests our ability to manipulate and compare fractions involving decimals. The key is to see if one fraction can be transformed into the other.
Step 2: Key Formula or Approach:
A key property of fractions is that if you multiply the numerator and the denominator by the same non-zero number, the value of the fraction remains unchanged. That is, \(\frac{a}{b} = \frac{a \times k}{b \times k}\) for \(k \neq 0\).
Step 3: Detailed Explanation:
Let's look at the fraction in Column B:
\[ \frac{0.027}{0.053} \]
We can multiply the numerator and the denominator by 10 to shift the decimal point one place to the right without changing the fraction's value:
\[ \frac{0.027 \times 10}{0.053 \times 10} = \frac{0.27}{0.53} \]
This resulting fraction is exactly the same as the fraction in Column A.
Alternatively, we can start with Column A and divide the numerator and denominator by 10:
\[ \frac{0.27 \div 10}{0.53 \div 10} = \frac{0.027}{0.053} \]
This shows that the quantity in Column A is equivalent to the quantity in Column B.
Step 4: Final Answer:
The quantity in Column A, \(\frac{0.27}{0.53}\), is equal to the quantity in Column B, \(\frac{0.027}{0.053}\). The two quantities are equal.