A decimeter (dm) is one-tenth of a meter. The diameter of Earth is 1.3 x 10^4 km. What is the diameter expressed in decimeters? 1.3 × 10^7 dm 1.3 × 10^11 dm 1.3 × 10^8 dm 1.3 × 10^5 dm
The Correct Answer and Explanation is:
Correct Answer: 1.3 × 10¹¹ dm
Step-by-Step Explanation:
We are asked to convert the diameter of Earth from kilometers (km) to decimeters (dm).
Given:
- Diameter of Earth = 1.3 × 10⁴ km
- 1 kilometer (km) = 1000 meters (m)
- 1 meter (m) = 10 decimeters (dm)
Step 1: Convert kilometers to meters
Since 1 km = 1000 m: 1.3×104 km=1.3×104×103 m=1.3×107 m1.3 \times 10^4 \, \text{km} = 1.3 \times 10^4 \times 10^3 \, \text{m} = 1.3 \times 10^7 \, \text{m}1.3×104km=1.3×104×103m=1.3×107m
Step 2: Convert meters to decimeters
Since 1 m = 10 dm: 1.3×107 m=1.3×107×10 dm=1.3×108 dm1.3 \times 10^7 \, \text{m} = 1.3 \times 10^7 \times 10 \, \text{dm} = 1.3 \times 10^8 \, \text{dm}1.3×107m=1.3×107×10dm=1.3×108dm
So, the correct value of Earth’s diameter expressed in decimeters is: 1.3×108 dm\boxed{1.3 \times 10^8 \, \text{dm}}1.3×108dm
Conclusion:
From the available options:
- 1.3 × 10⁷ dm — Incorrect, it misses one power of ten during the conversion from meters to decimeters.
- 1.3 × 10¹¹ dm — Incorrect, it adds extra powers of ten.
- 1.3 × 10⁸ dm — Correct, matches the correct conversion.
- 1.3 × 10⁵ dm — Incorrect, underestimates the size significantly.
Final Answer:
1.3 × 10⁸ dm is the correct conversion for Earth’s diameter from kilometers to decimeters.
This conversion process highlights the importance of carefully tracking unit relationships and properly handling powers of ten. Converting between different metric units relies on knowing their scale factors, such as 1 km being 1000 meters and 1 meter being 10 decimeters. The metric system simplifies these conversions with consistent factors based on powers of ten, making it efficient for large-scale scientific measurements like planetary diameters.
