Let's go through each part of your question step by step:
(A) To express the average distance from the Sun to Mercury in scientific notation, we start with the value 58,000,000 km.
To convert to scientific notation:
- Identify the significant figures: It will be 5.8.
- Count how many places the decimal point moves to the left to get it to the first significant figure (5.8): It moves 7 places to the left.
Thus, we write it as: \[ 5.8 \times 10^7 \text{ km} \]
(B) The diameter of a human hair is given as 0.0025 cm.
To convert this to scientific notation:
- Identify the significant figures: It will be 2.5.
- Count how many places the decimal point moves to the right to get it to the first significant figure (2.5): It moves 3 places to the right.
Thus, we write it as: \[ 2.5 \times 10^{-3} \text{ cm} \]
(C) To compare the measurements in Parts (A) and (B), we must ensure that both measurements are in the same units.
In this case:
- Convert either the distance from the Sun to Mercury (in km) to centimeters or the diameter of a human hair (in cm) to kilometers.
To convert 58,000,000 km to centimeters, we recall that 1 km = 100,000 cm. Therefore: \[ 58,000,000 \text{ km} \times 100,000 \text{ cm/km} = 5.8 \times 10^7 \text{ km} \times 10^5 \text{ cm/km} = 5.8 \times 10^{12} \text{ cm} \]
Now you can compare \(5.8 \times 10^{12} \text{ cm}\) (distance to Mercury) with \(2.5 \times 10^{-3} \text{ cm}\) (diameter of a human hair).
So, to summarize:
- (A) \(5.8 \times 10^7 \text{ km}\)
- (B) \(2.5 \times 10^{-3} \text{ cm}\)
- (C) Ensure both measurements are in the same units for comparison (e.g., convert km to cm).