MEASUREMENT
Interconverting compound SI units Convert the following measurement. g cm kg.m 6 8.1 x 10
The Correct Answer and Explanation is:
Let’s break down your request and clarify what needs to be converted.
You wrote:
“Convert the following measurement. g cm kg.m 6 8.1 x 10”
This seems to be an attempt to convert 8.1 × 10⁶ g·cm into kg·m.
✅ Step-by-Step Conversion:
We are given:
8.1 × 10⁶ g·cm
We want to convert this into:
kg·m
This involves converting grams (g) to kilograms (kg) and centimeters (cm) to meters (m).
🔁 Unit Conversion Factors:
- 1 kilogram (kg) = 1000 grams (g) → 1 kg1000 g\frac{1\ \text{kg}}{1000\ \text{g}}
- 1 meter (m) = 100 centimeters (cm) → 1 m100 cm\frac{1\ \text{m}}{100\ \text{cm}}
So the conversion becomes: 8.1×106 g\cdotpcm×(1 kg1000 g)×(1 m100 cm)8.1 \times 10^6\ \text{g·cm} \times \left( \frac{1\ \text{kg}}{1000\ \text{g}} \right) \times \left( \frac{1\ \text{m}}{100\ \text{cm}} \right)
Now simplify: =8.1×106×11000×1100=8.1×106×1100000=8.1×106105=8.1×101=81 kg\cdotpm= 8.1 \times 10^6 \times \frac{1}{1000} \times \frac{1}{100} = 8.1 \times 10^6 \times \frac{1}{100000} = \frac{8.1 \times 10^6}{10^5} = 8.1 \times 10^1 = 81\ \text{kg·m}
✅ Final Answer:
81 kg·m
📘 Explanation (300+ words):
Interconverting compound SI units involves converting both parts of a unit expression. In this case, the original unit is g·cm (gram-centimeter), and we need to convert it to kg·m (kilogram-meter). This type of conversion is common in physics and engineering when dealing with quantities like torque or work, which may initially be calculated using different units.
To perform the conversion accurately, we treat each unit independently. The metric system is based on powers of ten, which makes conversions straightforward using multiplication or division.
- Convert grams (g) to kilograms (kg):
- Since 1 kilogram is equal to 1000 grams, you divide the number of grams by 1000.
- Mathematically: value in kg=value in g1000\text{value in kg} = \frac{\text{value in g}}{1000}
- Convert centimeters (cm) to meters (m):
- Since 1 meter is equal to 100 centimeters, you divide the number of centimeters by 100.
- Mathematically: value in m=value in cm100\text{value in m} = \frac{\text{value in cm}}{100}
When both these conversions are applied together, you are dividing the original value by 1000 (for grams) and by 100 (for centimeters), giving a total division by 100,000.
So, for the measurement 8.1 × 10⁶ g·cm, we convert it by dividing by 100,000, resulting in 81 kg·m.
Understanding how to interconvert compound SI units is important because scientific and technical fields often require standard units for clear communication and accurate calculations. By following a systematic approach and using conversion factors correctly, you ensure consistency and precision in your results.