From Nanometer/Square Second to Hectometer/Square Second: Simplified Conversion for 31.5

When working with measurements in physics, engineering, or other sciences, it’s not uncommon to encounter various units of length and time that need conversion. These conversions are essential for standardizing measurements and ensuring consistency in calculations. One such conversion involves changing units from nanometer per square second (nm/s²) to hectometer per square second (hm/s²). This article will provide a simplified explanation of how to convert the value 31.5 nm/s² into hectometer per square second, while outlining the necessary steps for such transformations.

Understanding the Units

Before diving into the conversion process, let’s define the units involved:

1. Nanometer (nm): A nanometer is one billionth of a meter (1 nm = 10⁻⁹ meters).
2. Hectometer (hm): A hectometer is one hundred meters (1 hm = 100 meters).
3. Square second (s²): A unit of time squared, commonly used to measure acceleration, is consistent across both nanometer and hectometer conversions.

The Conversion Process

To convert from nanometer per square second (nm/s²) to hectometer per square second (hm/s²), we need to account for the difference in length between nanometers and hectometers. Let’s break it down step-by-step.

1. Convert Nanometers to Hectometers:
   • We know that 1 hectometer equals 100 meters, and 1 nanometer equals 10⁻⁹ meters.
   • To convert from nanometers to hectometers, we can set up the following relationship:
   1 nm=10−9 m,1 hm=100 m1 \text{ nm} = 10^{-9} \text{ m}, \quad 1 \text{ hm} = 100 \text{ m}1 nm=10−9 m,1 hm=100 mSo, to convert 1 nanometer to hectometer:1 nm=10−9 m=10−9×10−2 hm=10−11 hm1 \text{ nm} = 10^{-9} \text{ m} = 10^{-9} \times 10^{-2} \text{ hm} = 10^{-11} \text{ hm}1 nm=10−9 m=10−9×10−2 hm=10−11 hmTherefore, 1 nanometer is equal to 10−1110^{-11}10−11 hectometers.
2. Apply the Conversion to the Given Value: The value we are working with is 31.5 nanometer per square second (31.5 nm/s²). To convert this to hectometer per square second (hm/s²), we multiply by the conversion factor:31.5 nm/s²=31.5×10−11 hm/s²31.5 \text{ nm/s²} = 31.5 \times 10^{-11} \text{ hm/s²}31.5 nm/s²=31.5×10−11 hm/s²Simplifying this:31.5×10−11=3.15×10−10 hm/s²31.5 \times 10^{-11} = 3.15 \times 10^{-10} \text{ hm/s²}31.5×10−11=3.15×10−10 hm/s²

Final Answer

Thus, 31.5 nanometer per square second is equivalent to 3.15×10−103.15 \times 10^{-10}3.15×10−10 hectometer per square second.

Conclusion

The conversion from nanometer per square second to hectometer per square second is a straightforward process once the relationship between nanometers and hectometers is understood. By following the steps outlined above, we can easily convert the value 31.5 nm/s² to its hectometer per square second equivalent, which is 3.15×10−103.15 \times 10^{-10}3.15×10−10 hm/s². Such conversions are essential in various fields where precise measurements and standard units are crucial for calculations and analyses.