Question

Column A	Column B
\(\frac{1}{11}\)	0.09

 

Hint:

Cross-multiplication is often the fastest and most error-proof way to compare two simple fractions, as it avoids long division and dealing with repeating decimals.

Answer 1

Step 1: Understanding the Concept:
This question requires the comparison of a fraction and a decimal. To compare them accurately, we should convert them to a common format.
Step 2: Key Formula or Approach:
We can either convert the fraction to a decimal or the decimal to a fraction. Alternatively, for comparing fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), we can use cross-multiplication: compare \(a \times d\) and \(b \times c\).
Step 3: Detailed Explanation:
Method 1: Convert Fraction to Decimal
To convert \(\frac{1}{11}\) to a decimal, we perform the division 1 \(\div\) 11.
\[ 1 \div 11 = 0.090909... \] We are comparing \(0.0909...\) (Column A) with 0.09 (Column B).
Since \(0.0909...\) is greater than 0.0900, the quantity in Column A is greater.
Method 2: Convert Decimal to Fraction and Cross-Multiply
The decimal 0.09 is equivalent to the fraction \(\frac{9}{100}\).
Now we compare \(\frac{1}{11}\) (Column A) with \(\frac{9}{100}\) (Column B).
We cross-multiply the numerators and denominators:
For Column A: \(1 \times 100 = 100\).
For Column B: \(11 \times 9 = 99\).
Since \(100>99\), the fraction corresponding to the 100 (\(\frac{1}{11}\)) is greater.
Step 4: Final Answer:
Both methods show that \(\frac{1}{11}\) is greater than 0.09. The quantity in Column A is greater.