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.
