How many micrometers make up 1.0 km
The Correct Answer and Explanation is:
To convert kilometers (km) to micrometers (µm), we need to break down the units systematically.
- Start with the given value: 1.0 km.
- We know that 1 kilometer is equal to 1,000 meters (1 km = 1,000 m).
- Convert meters to micrometers:
- 1 meter is equivalent to 1,000,000 micrometers (1 m = 1,000,000 µm).
Thus, to convert kilometers to micrometers, we multiply by the conversion factors for kilometers to meters, and then meters to micrometers:1.0 km×1,000 m1 km×1,000,000 μm1 m1.0 \, \text{km} \times \frac{1,000 \, \text{m}}{1 \, \text{km}} \times \frac{1,000,000 \, \mu\text{m}}{1 \, \text{m}}1.0km×1km1,000m×1m1,000,000μm
Now, perform the multiplication:1.0×1,000×1,000,000=1,000,000,000 μm1.0 \times 1,000 \times 1,000,000 = 1,000,000,000 \, \mu\text{m}1.0×1,000×1,000,000=1,000,000,000μm
So, 1.0 km = 1,000,000,000 micrometers (1.0 × 10^9 µm).
Explanation:
The conversion process involves multiplying by the respective factors of 1,000 (for kilometers to meters) and 1,000,000 (for meters to micrometers). These are basic metric system conversions where the metric system operates on powers of 10, which makes such conversions relatively simple. In this case, we multiplied the two factors to get the final result, which is 1.0 km = 1,000,000,000 µm or 1.0 × 10^9 micrometers.
This result illustrates how the metric system’s consistent scaling by factors of 10 allows for straightforward unit conversions.
