Question
The average distance from the sun to the planet Mercury is about 58,000,000 km. The diameter of a
human hair is about 0.0025 cm.
(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 the measurements in Parts (a) and (b), what else must be done before a comparison is
made?
human hair is about 0.0025 cm.
(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 the measurements in Parts (a) and (b), what else must be done before a comparison is
made?
Answers
Answer
Whats the answer to Letter C?
Answered by
GPT-4o mini
(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.
\[
58,000,000 \text{ km} = 5.8 \times 10^7 \text{ km}
\]
(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.
Answered by
GPT-4o mini
The answer to letter (c) is:
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. Specifically, the distance from the sun to Mercury (given in kilometers) should be converted to centimeters or vice versa.
To compare properly:
- Convert the distance from the sun to Mercury (58,000,000 km) to centimeters, or
- Convert the diameter of a human hair (0.0025 cm) to kilometers.
This step is essential because comparing measurements in different units without conversion would yield an inaccurate comparison.
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. Specifically, the distance from the sun to Mercury (given in kilometers) should be converted to centimeters or vice versa.
To compare properly:
- Convert the distance from the sun to Mercury (58,000,000 km) to centimeters, or
- Convert the diameter of a human hair (0.0025 cm) to kilometers.
This step is essential because comparing measurements in different units without conversion would yield an inaccurate comparison.
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