What is the ratio between 0.02 and 0.002?

Appeared in: OSSSC Nursing Officer-2021

Explanation

A ratio compares two quantities. The ratio of 'a' to 'b' can be written as a/b.
To find the ratio of 0.02 to 0.002, set it up as a fraction: 0.02 / 0.002.
To simplify the decimal fraction, multiply both the numerator and denominator by 1000 to convert them to whole numbers. This gives 20 / 2.
Simplifying the fraction 20/2 gives 10, which is expressed as the ratio 10:1.

Option A: This ratio is equivalent to 1/10 or 0.1. The calculated ratio is 10.
Option B: This ratio is equivalent to 1/100 or 0.01. The calculated ratio is 10.
Option C: This ratio is equivalent to 100/1 or 100. The calculated ratio is 10.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating ratios with decimal numbers as background academic context rather than a clinical decision trigger.
Basic numeracy and calculation skills are fundamental for safe nursing practice, especially in medication dosage calculations, fluid balance monitoring, and interpreting lab results.
Errors in decimal placement can lead to significant medication errors, potentially causing severe harm to patients. For example, administering 2.0 mg instead of 0.2 mg is a tenfold overdose.
What if? If the question asked for the ratio between 0.002 and 0.02, the order would be reversed, resulting in the fraction 0.002 / 0.02, which simplifies to 2/20 or 1/10, making the ratio 1:10.

How to Approach the Question

First, identify the two numbers for which the ratio is required. Note the order in which they are presented.
Write the ratio as a fraction, with the first number as the numerator and the second number as the denominator (e.g., a/b for the ratio of a to b).
If the numbers are decimals, find the number with the most decimal places. Multiply both the numerator and denominator by the power of 10 needed to make that number a whole number (e.g., multiply by 100 for two decimal places, 1000 for three).
Simplify the resulting fraction of whole numbers to its simplest form.
Convert the simplified fraction back into ratio format (e.g., x/y becomes x:y).

Concept Tested & Keywords

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