Which of the following quantities is equivalent to 3.7 cm?
A. 3.7×10⁻⁵ km
B. 3.7×10⁵ μm
C. 3.7×10⁻² mm
D. 3.7×10² mm
E. 3.7×10⁻³ m
The Correct Answer and Explanation is:
The correct answer is E. 3.7×10⁻³ m.
Explanation:
To solve this, let’s convert 3.7 cm into various units of length and determine which option is equivalent.
Step 1: Convert 3.7 cm to meters (m).
We know that 1 cm = 0.01 m (since 1 m = 100 cm). So to convert 3.7 cm to meters:
[
3.7 \, \text{cm} = 3.7 \times 0.01 \, \text{m} = 0.037 \, \text{m}
]
Step 2: Convert 0.037 m to other units in the options.
- Option A: (3.7 \times 10^{-5}) km:
- To convert meters to kilometers, we use the conversion factor: 1 km = 1000 m.
- Thus, (3.7 \, \text{cm} = 0.037 \, \text{m} = 0.037 \div 1000 = 3.7 \times 10^{-5} \, \text{km}).
- This is correct but doesn’t match the other options since it’s in kilometers.
- Option B: (3.7 \times 10^5 \, \mu\text{m}) (micrometers):
- To convert meters to micrometers (μm), we know that 1 m = (10^6 \, \mu\text{m}).
- So, (0.037 \, \text{m} = 0.037 \times 10^6 \, \mu\text{m} = 37,000 \, \mu\text{m} = 3.7 \times 10^4 \, \mu\text{m}).
- This is incorrect because (3.7 \times 10^5 \, \mu\text{m}) is too large.
- Option C: (3.7 \times 10^{-2}) mm (millimeters):
- To convert meters to millimeters (mm), we know that 1 m = 1000 mm.
- So, (0.037 \, \text{m} = 0.037 \times 1000 \, \text{mm} = 37 \, \text{mm}), which is much larger than (3.7 \times 10^{-2} \, \text{mm}), making this option incorrect.
- Option D: (3.7 \times 10^2 \, \text{mm}):
- Again, we know (0.037 \, \text{m} = 37 \, \text{mm}), which is not (3.7 \times 10^2 = 370 \, \text{mm}).
- This option is incorrect because it is too large.
- Option E: (3.7 \times 10^{-3} \, \text{m}):
- This directly matches the value we obtained from the conversion in step 1. (0.037 \, \text{m} = 3.7 \times 10^{-3} \, \text{m}).
Thus, E. 3.7×10⁻³ m is the correct answer.