To determine how many times greater the diameter of a dime is compared to the diameter of a strand of human hair, we need to use the following steps:
1. Identify the diameters:
- The diameter of the dime is [tex]\( 17.91 \)[/tex] mm.
- The diameter of the strand of human hair is [tex]\( 6.0 \times 10^{-2} \)[/tex] mm.
2. Calculate the ratio:
- To find out how many times greater the diameter of the dime is compared to the diameter of the strand of human hair, we divide the diameter of the dime by the diameter of the strand of human hair:
[tex]\[
\text{Ratio} = \frac{\text{Diameter of dime}}{\text{Diameter of hair}} = \frac{17.91 \, \text{mm}}{6.0 \times 10^{-2} \, \text{mm}}
\][/tex]
3. Perform the division:
- Simplify the expression:
[tex]\[
\text{Ratio} = \frac{17.91}{6.0 \times 10^{-2}}
\][/tex]
- To make the division simpler, recall that dividing by [tex]\( 10^{-2} \)[/tex] is the same as multiplying by [tex]\( 10^2 \)[/tex]:
[tex]\[
\text{Ratio} = 17.91 \times \frac{1}{6.0} \times 10^2
\][/tex]
4. Calculate the numerical values:
- First, divide [tex]\( 17.91 \)[/tex] by [tex]\( 6.0 \)[/tex]:
[tex]\[
\frac{17.91}{6.0} = 2.985
\][/tex]
- Then, multiply the result by [tex]\( 10^2 \)[/tex]:
[tex]\[
2.985 \times 10^2 = 298.5
\][/tex]
So, the diameter of a dime is 298.5 times greater than the diameter of the strand of human hair.
Therefore, the correct answer in scientific notation can be matched with the available options:
- [tex]\( 2.985 \times 10^2 \)[/tex]
So, the correct answer is:
[tex]\[
2.985 \times 10^2
\][/tex]
