The ratio 80 cm to 2 m is?

Appeared in: RML Lucknow - 2021

Explanation

To compare two quantities in a ratio, they must first be converted to the same unit.
The conversion from meters to centimeters is: 1 meter = 100 centimeters. Therefore, 2 meters = 2 × 100 = 200 cm.
With both quantities in centimeters, the ratio is 80 cm to 200 cm, which is written as 80:200.
To simplify the ratio, both numbers are divided by their greatest common divisor, which is 40.
Dividing both sides by 40 (80 ÷ 40 and 200 ÷ 40) results in the simplified ratio of 2:5.

Option B: This ratio is equivalent to 2:5, but it is not in its simplest form. In mathematics, ratios should always be presented in their most reduced form unless otherwise specified.
Option C: This ratio is incorrect. A ratio of 3:5 would be equivalent to 120:200, not 80:200.
Option D: This ratio is incorrect. A ratio of 4:5 would be equivalent to 160:200, not 80:200.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating and simplifying ratios with different units of measurement as background academic context rather than a clinical decision trigger.
Understanding ratios is a fundamental math skill essential for safe nursing practice, particularly in medication dosage calculations and preparing solutions.
For example, when preparing a solution from a concentrate, nurses must use ratios to determine the correct amount of solute and solvent (e.g., mixing 1 part medication with 4 parts sterile water is a 1:4 ratio).
Errors in understanding or calculating ratios can lead to significant medication errors, potentially harming the patient. This basic math skill is a cornerstone of patient safety.

How to Approach the Question

First, identify the two quantities being compared in the ratio: 80 cm and 2 m.
Recognize that the units of measurement are different (centimeters and meters). The most critical first step is to convert them to a common unit.
Choose a unit to convert to. It is generally easier to convert the larger unit (meters) to the smaller unit (centimeters) to avoid decimals. Recall or look up the conversion factor: 1 m = 100 cm.
Apply the conversion: 2 m × 100 cm/m = 200 cm.
Now, write the ratio using the same units: 80:200.
Simplify the ratio by finding the largest number that divides both 80 and 200 (the greatest common divisor). In this case, the GCD is 40.

Concept Tested & Keywords

Concept Tested: Calculating and simplifying ratios with different units of measurement.
Stem keywords: ratio, 80 cm, 2 m
Lead-in keywords: is?
Negative lead-in flag: false

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