Convert 14.5 inches to cm. Which of the following is the correct set up for this conversion?
14.5 in x (1 in / 0.254 cm)
14.5 in x (1 in / 2.54 cm) =
14.5 in x (0.254 cm / 1 in) =
14.5 in x (2.54 cm / 1 in)
The correct answer and explanation is :
The correct setup for converting 14.5 inches to centimeters is:
✅ 14.5 in × (2.54 cm / 1 in)
Detailed Explanation:
When you are converting between units, you use conversion factors that relate the two units.
In this case, you need to know the basic fact that:
- 1 inch = 2.54 centimeters
This means that 2.54 centimeters is equal to 1 inch.
Thus, the conversion factor is either:
- ( \frac{2.54\ \text{cm}}{1\ \text{in}} ) or ( \frac{1\ \text{in}}{2.54\ \text{cm}} )
But how do you choose the right one?
You set up your conversion so that the units you want to cancel are opposite each other.
Since you are starting with inches (in), you want to cancel out inches and end up with centimeters (cm).
Therefore, inches must be in the denominator, and centimeters in the numerator.
- Start: 14.5 in × (conversion factor)
- Setup: 14.5 in × ( 2.54 cm / 1 in )
When you multiply:
[
14.5\ \text{in} \times \frac{2.54\ \text{cm}}{1\ \text{in}}
]
the “inches” cancel out:
[
\text{(in)} \div \text{(in)} = 1
]
leaving only centimeters:
[
14.5 \times 2.54 = 36.83\ \text{cm}
]
Why the Other Choices Are Incorrect:
- 14.5 in × (1 in / 0.254 cm) → This would convert cm to in, not in to cm. (Also, the value 0.254 is wrong.)
- 14.5 in × (1 in / 2.54 cm) → Again, this would incorrectly cancel cm, not in, leading to wrong units.
- 14.5 in × (0.254 cm / 1 in) → The setup is correct in structure (cm over in), but the number is wrong (should be 2.54, not 0.254).
Final Answer:
✅ 14.5 in × (2.54 cm / 1 in)
Which calculates to:
[
14.5\ \text{in} \times 2.54\ \text{cm/in} = 36.83\ \text{cm}
]