What is the ratio between 0.02 and 0.002?

Appeared in: HPSSC - 2015

Explanation

A ratio compares two quantities. The ratio of 0.02 to 0.002 is written as the fraction 0.02/0.002.
To simplify a fraction with decimals, multiply both the numerator and the denominator by the same power of 10. Here, we multiply by 1000 to convert both numbers to whole numbers.
The calculation is: (0.02 × 1000) / (0.002 × 1000) = 20 / 2.
Simplifying the fraction 20/2 gives 10/1.
The fraction 10/1 is expressed as the ratio 10:1.

Option A: This is the inverse of the correct ratio.
Option B: This incorrect ratio likely results from a decimal placement error during calculation.
Option C: This is the inverse of the other incorrect option (100:1) and also results from a calculation error involving decimal points.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the ratio between two decimal numbers as background academic context rather than a clinical decision trigger.
Mastery of ratio calculations is critical for patient safety in nursing, especially for medication dosage. An error in placing a decimal can lead to a tenfold or hundredfold overdose or underdose.
For example, preparing a drug solution might require a 1:10 dilution. Miscalculating this as 10:1 would result in a solution that is 100 times more concentrated, which could be fatal.
What if? If a nurse needed to prepare a 1:100 bleach solution for disinfection and miscalculated it as 1:10, the solution would be ten times stronger than necessary, potentially damaging surfaces and causing respiratory irritation to patients and staff.

How to Approach the Question

First, identify that the question asks for a ratio between two numbers.
Represent the ratio as a fraction, with the first number (0.02) as the numerator and the second number (0.002) as the denominator.
To eliminate the decimals, multiply both the numerator and denominator by the power of 10 that corresponds to the largest number of decimal places (in this case, 1000 for three places).
Simplify the resulting fraction of whole numbers (20/2).
Convert the simplified fraction (10/1) back into the ratio format (10:1) to find the correct option.

Concept Tested & Keywords

QirpSGJVHsMKU9WSum-Ydq

Practise the full HPSSC - 2015

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