A conversion factor set up correctly to convert 15 inches to centimeters is
a. 100 cm/1 m
b. 2.54 cm/1 inch
C . 10 cm/1 inch
C. 1 cm/10 mm
D. 1 inch/2.54 cm
The Correct Answer and Explanation is :
The correct answer is b. 2.54 cm/1 inch.
Explanation:
To convert 15 inches to centimeters, we need to use a conversion factor between inches and centimeters. The relationship between inches and centimeters is given by the fact that 1 inch = 2.54 cm. This conversion factor allows us to multiply the number of inches by 2.54 to convert to centimeters.
Step-by-Step Conversion:
- Start with the quantity to convert, which is 15 inches.
- Use the conversion factor 2.54 cm/1 inch to convert inches to centimeters.
- Set up the conversion like this:
[
15 \, \text{inches} \times \frac{2.54 \, \text{cm}}{1 \, \text{inch}} = 15 \times 2.54 = 38.1 \, \text{cm}
] - Thus, 15 inches is equal to 38.1 centimeters.
Why the Other Options Are Incorrect:
- a. 100 cm/1 m: This conversion factor is used to convert meters to centimeters, not inches to centimeters. It’s irrelevant to this conversion.
- c. 10 cm/1 inch: This conversion factor is incorrect because 1 inch is equal to 2.54 cm, not 10 cm.
- d. 1 cm/10 mm: This conversion factor is for converting between centimeters and millimeters, not inches to centimeters.
- e. 1 inch/2.54 cm: This is the inverse of the correct conversion factor. While this could be useful to convert centimeters back to inches, it is not suitable for converting inches to centimeters.
In conclusion, 2.54 cm/1 inch is the correct conversion factor to use when converting inches to centimeters. By multiplying the given number of inches by this conversion factor, you can easily find the equivalent length in centimeters.