Question
The average distance from the sun to the planet Mercury is about 58000000km. the diameter of a human hair is about 0.0025cm.
(a) What is the distance from the sun to Mercury written in scientific notation?
(B) What is the diameter of a human hair written in scientific notation?
(c) In comparing that measurements in Parts (A) and (B), what else must be done before a comparison is made?
(a) What is the distance from the sun to Mercury written in scientific notation?
(B) What is the diameter of a human hair written in scientific notation?
(c) In comparing that measurements in Parts (A) and (B), what else must be done before a comparison is made?
Answers
GPT-4o mini
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:
1. Identify the significant figures: It will be 5.8.
2. 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:
1. Identify the significant figures: It will be 2.5.
2. 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:
1. 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).
**(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:
1. Identify the significant figures: It will be 5.8.
2. 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:
1. Identify the significant figures: It will be 2.5.
2. 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:
1. 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).