Unit conversion is an essential mathematical skill, especially in scientific and engineering applications. Converting values accurately ensures precision in calculations and consistency in data representation. This article explains how to convert 0.30 femtometers per second squared (fm/s²) into hectometers per second squared (hm/s²) with accuracy.
Understanding the Units
Before performing the conversion, let’s break down the units involved:
- Femtometer (fm): A femtometer is 10−1510^{-15}10−15 meters, commonly used in atomic and nuclear physics to measure extremely small distances.
- Hectometer (hm): A hectometer is 10210^2102 meters, equivalent to 100 meters.
- Second squared (s²): The unit of time remains unchanged during acceleration conversions.
Thus, the goal is to convert 0.30 fm/s² to hm/s², which means we need to express femtometers in terms of hectometers.
Conversion Factor
We use the following relationship between femtometers and hectometers:1 fm=10−15 m1 \text{ fm} = 10^{-15} \text{ m}1 fm=10−15 m1 hm=102 m1 \text{ hm} = 10^2 \text{ m}1 hm=102 m
Since we want to express femtometers in terms of hectometers, we divide both sides by 10210^2102:1 fm=10−15 m=10−17 hm1 \text{ fm} = 10^{-15} \text{ m} = 10^{-17} \text{ hm}1 fm=10−15 m=10−17 hm
Applying the Conversion
Now, we multiply 0.30 fm/s² by the conversion factor 10−1710^{-17}10−17 to obtain the value in hm/s²:0.30×10−17 hm/s²=3.0×10−18 hm/s²0.30 \times 10^{-17} \text{ hm/s²} = 3.0 \times 10^{-18} \text{ hm/s²}0.30×10−17 hm/s²=3.0×10−18 hm/s²
Final Answer
0.30 fm/s²=3.0×10−18 hm/s²0.30 \text{ fm/s²} = 3.0 \times 10^{-18} \text{ hm/s²}0.30 fm/s²=3.0×10−18 hm/s²
This is the accurate conversion result.
Conclusion
Converting acceleration units from femtometers per second squared (fm/s²) to hectometers per second squared (hm/s²) involves understanding metric prefixes and applying appropriate conversion factors. By following a systematic approach, we determined that 0.30 fm/s² is equal to 3.0×10−183.0 \times 10^{-18}3.0×10−18 hm/s² with accuracy. This method can be applied to other unit conversions for precise scientific calculations.