A bike wheel is 26 inches in diameter. What is the bike wheel's diameter in millimeters (1 inch = 25.4 millimeters)?

A. [tex]\(26 \text{ inches} \left(\frac{1 \text{ inch}}{25.4 \text{ millimeters}}\right)\)[/tex]

B. [tex]\(26 \text{ inches} \left(\frac{25.4 \text{ millimeters}}{1 \text{ inch}}\right)\)[/tex]

C. [tex]\(25.4 \text{ inches} \left(\frac{1 \text{ millimeter}}{26 \text{ inches}}\right)\)[/tex]

D. [tex]\(26 \text{ inches} \left(\frac{1 \text{ millimeter}}{25.4 \text{ inches}}\right)\)[/tex]



Answer :

Given that the bike wheel's diameter is 26 inches and that 1 inch is equivalent to 25.4 millimeters, we need to convert the diameter from inches to millimeters.

To perform this conversion, we will use the correct conversion factor which is [tex]\(\frac{25.4 \text{ millimeters}}{1 \text{ inch}}\)[/tex]. This means every inch is replaced by 25.4 millimeters.

Here's the step-by-step solution:

1. Start with the diameter in inches: 26 inches.
2. Multiply this diameter by the conversion factor [tex]\(\frac{25.4 \text{ millimeters}}{1 \text{ inch}}\)[/tex]:

[tex]\[ 26 \text{ inches} \times \left( \frac{25.4 \text{ millimeters}}{1 \text{ inch}} \right) \][/tex]

3. The inches units cancel out, leaving the expression in millimeters:

[tex]\[ 26 \times 25.4 \text{ millimeters} \][/tex]

4. Perform the multiplication:

[tex]\[ 26 \times 25.4 = 660.4 \text{ millimeters} \][/tex]

Thus, the diameter of the bike wheel is [tex]\(660.4\)[/tex] millimeters. The correct choice from the given options is:

[tex]\[ \text{26 inches} \left(\frac{25.4 \text{ millimeters}}{1 \text{ inch}} \right) \][/tex]

which results in [tex]\(660.4\)[/tex] millimeters.