(a) To write the average distance from the sun to Mercury in scientific notation, we express \( 58,000,000 \) km as follows:
\[ 58,000,000 \text{ km} = 5.8 \times 10^7 \text{ km} \]
(b) To express the diameter of a human hair, which is \( 0.0025 \) cm, in scientific notation, we write:
\[ 0.0025 \text{ cm} = 2.5 \times 10^{-3} \text{ cm} \]
(c) Before making a comparison between the measurements in Parts (a) and (b), it is necessary to ensure that both measurements are in the same units. The distance from the sun to Mercury is given in kilometers, and the diameter of a human hair is given in centimeters. To make an accurate comparison, we need to convert one measurement to the other's unit (e.g., converting kilometers to centimeters or centimeters to kilometers).
Recall that:
- \( 1 \text{ km} = 100,000 \text{ cm} = 10^5 \text{ cm} \)
So to convert the distance from Mercury to centimeters: \[ 5.8 \times 10^7 \text{ km} = 5.8 \times 10^7 \times 10^5 \text{ cm} = 5.8 \times 10^{12} \text{ cm} \]
Now, both measurements can be directly compared.
1 answer