A suitcase had a width of 55 cm. Which unit conversion fraction should you use to find the width in inches? A. 1 cm/2.54 in B. 1 in/2.54 cm C. 2.54 cm/1 in D. 1 in/1 cm
The correct answer and explanation is:
Correct Answer: C. 2.54 cm / 1 in
Explanation (300 words):
When converting units, it’s important to choose a conversion factor (also called a unit conversion fraction) that helps you cancel out the original units and convert to the desired units. In this case, the suitcase has a width of 55 cm, and you want to convert centimeters (cm) to inches (in).
The standard relationship between centimeters and inches is:
1 inch = 2.54 centimeters
Now, you want to convert from centimeters to inches. That means you want centimeters to cancel out, leaving you with inches. To do this, you need to divide by centimeters and multiply by inches.
So, you use the fraction:
1 in / 2.54 cm
But if we rewrite this fraction so the centimeters are on top and inches on the bottom, it looks like:
C. 2.54 cm / 1 in
This is the standard conversion factor. However, this particular fraction helps when you’re converting inches to centimeters. But you are going from centimeters to inches, so to get the correct orientation, you need the reciprocal of this:
Correct fraction: 1 in / 2.54 cm → which is Answer B, not C.
Upon double-checking, there’s a mistake in the answer given earlier.
✅ Correct Answer (Updated): B. 1 in / 2.54 cm
Why B is Correct:
- You start with: 55 cm
- Multiply by: (1 in / 2.54 cm)
- Calculation:
55 cm×1 in2.54 cm=≈21.65 in55 \, \text{cm} \times \frac{1 \, \text{in}}{2.54 \, \text{cm}} = \approx 21.65 \, \text{in} - The cm units cancel, and you’re left with inches.
Summary:
- Always use a conversion factor where the original unit cancels out.
- For cm to inches, the correct fraction is 1 in / 2.54 cm → Answer B.