Converting units of measurement, especially in the metric system, is a fundamental skill in science, engineering, and daily life. This article will guide you through the process of converting 31.02 hectometer per square second (hm/s²) into centimeter per square second (cm/s²), a task that requires understanding the relationship between hectometers, centimeters, and how they are measured in square terms.
Understanding the Units
Before diving into the conversion, it’s essential to break down the units involved:
- Hectometer (hm): A hectometer is equal to 100 meters, so: 1 hm=100 m1 \, \text{hm} = 100 \, \text{m}1hm=100m
- Centimeter (cm): A centimeter is 1/100th of a meter, so: 1 cm=1100 m1 \, \text{cm} = \frac{1}{100} \, \text{m}1cm=1001m
When these units are squared (since we are working with “per square second” in the context), we need to consider the square of the conversion factor:
- 1 hm2=(100 m)2=10,000 m21 \, \text{hm}^2 = (100 \, \text{m})^2 = 10,000 \, \text{m}^21hm2=(100m)2=10,000m2
- 1 cm2=(1100 m)2=0.0001 m21 \, \text{cm}^2 = \left( \frac{1}{100} \, \text{m} \right)^2 = 0.0001 \, \text{m}^21cm2=(1001m)2=0.0001m2
Thus, the conversion from hectometers to centimeters involves multiplying by a factor of 1002100^21002 or 10,000, as we are converting both linear and area units.
Step-by-Step Conversion
The objective is to convert 31.02 hectometer per square second (hm/s²) to centimeter per square second (cm/s²). To do this, follow these steps:
- Convert the hectometer to centimeter: Since 1 hectometer equals 100 meters, and 1 meter equals 100 centimeters, we have: 1 hm=100×100 cm=10,000 cm1 \, \text{hm} = 100 \times 100 \, \text{cm} = 10,000 \, \text{cm}1hm=100×100cm=10,000cm
- Square the conversion factor: As we are dealing with area units, square the factor: 1 hm2=10,0002 cm2=100,000,000 cm21 \, \text{hm}^2 = 10,000^2 \, \text{cm}^2 = 100,000,000 \, \text{cm}^21hm2=10,0002cm2=100,000,000cm2
- Multiply by the given value: Now, multiply 31.02 hectometer per square second by the conversion factor for both the linear and area conversions: 31.02 hm/s2=31.02×100,000,000 cm/s231.02 \, \text{hm/s}^2 = 31.02 \times 100,000,000 \, \text{cm/s}^231.02hm/s2=31.02×100,000,000cm/s2 31.02 hm/s2=3,102,000,000 cm/s231.02 \, \text{hm/s}^2 = 3,102,000,000 \, \text{cm/s}^231.02hm/s2=3,102,000,000cm/s2
Final Answer
Thus, 31.02 hectometer per square second (hm/s²) is equal to 3,102,000,000 centimeter per square second (cm/s²).
Conclusion
The process of converting from hectometer per square second to centimeter per square second involves understanding the conversion factors between hectometers and centimeters and applying these to the square terms in the unit. This example shows how to easily convert between large metric units and is helpful for various applications, including physics and engineering calculations.