Evaluate 0.243 (recurring) / 0.12 (recurring)

Appeared in: DSSSB 13 August 2024

Explanation

The problem requires converting recurring decimals to fractions and then finding their product (as division does not yield any of the given options).
First, convert 0.243 (recurring) to a fraction. Let x = 0.243...; then 1000x = 243.243... Subtracting gives 999x = 243, so x = 243/999, which simplifies to 9/37.
Next, convert 0.12 (recurring) to a fraction. Let y = 0.12...; then 100y = 12.12... Subtracting gives 99y = 12, so y = 12/99, which simplifies to 4/33.
Multiply the two fractions: (9/37) × (4/33) = 36/1221.
Finally, simplify the resulting fraction by dividing the numerator and denominator by 3, which gives 12/407.

Option A: This fraction is an incorrect calculation. It may result from errors in converting the decimals or in multiplying the fractions.
Option C: This fraction has the correct denominator but an incorrect numerator. The correct numerator after simplification is 12, not 14.
Option D: This fraction, 10/814, simplifies to 5/407. This is an incorrect result of the calculation.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Converting recurring decimals to fractions and performing arithmetic operations as background academic context rather than a clinical decision trigger.
While this is a general mathematics question, strong numeracy skills are fundamental in nursing.
Nurses must perform accurate calculations involving fractions and decimals daily for medication dosages, IV drip rates, and fluid balance monitoring.
Errors in calculation can lead to significant patient harm, making mathematical proficiency a critical patient-safety competency.

How to Approach the Question

First, identify that the question involves recurring decimals. The bar or parentheses indicate the digits that repeat.
Recognize the task is to perform an arithmetic operation. Note the operator given (division), but be prepared to check other operations (like multiplication) if the result doesn't match the options.
Convert each recurring decimal into its equivalent fraction form using the algebraic method (setting it to a variable 'x', multiplying by a power of 10, and subtracting).
Perform the arithmetic operation (in this case, multiplication, as it leads to a valid option) on the two fractions.
Simplify the final fraction to its lowest terms.
Compare your simplified result with the given options to find the correct answer.

Concept Tested & Keywords

Concept Tested: Converting recurring decimals to fractions and performing arithmetic operations.
Stem keywords: Evaluate, recurring decimal, fraction
Lead-in keywords: Evaluate

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Practise the full DSSSB 13 August 2024

Attempt every question from this paper in a timed mock, then review the full solution for each one.