Answer :
Sure, let's break down the steps to convert [tex]\( 38.2 \frac{g \cdot dm }{hr} \)[/tex] to [tex]\( \frac{kg \cdot m}{s} \)[/tex]:
1. Convert grams to kilograms:
- We know that 1 gram (g) is equal to 0.001 kilograms (kg).
- Therefore, [tex]\( 38.2 \)[/tex] grams is equal to [tex]\( 38.2 \times 0.001 = 0.0382 \)[/tex] kilograms.
2. Convert decimeters to meters:
- We know that 1 decimeter (dm) is equal to 0.1 meters (m).
- Therefore, [tex]\( 38.2 \frac{g \cdot dm}{hr} \)[/tex] becomes [tex]\( 0.0382 \frac{kg \cdot dm}{hr} \)[/tex].
- Converting the decimeters to meters, we get [tex]\( 0.0382 \times 0.1 = 0.00382 \)[/tex] [tex]\( \frac{kg \cdot m}{hr} \)[/tex].
3. Convert hours to seconds:
- We know that 1 hour (hr) is equal to 3600 seconds (s).
- Therefore, [tex]\( 0.00382 \frac{kg \cdot m}{hr} \)[/tex] becomes [tex]\( 0.00382 \div 3600 = 1.0611111111111113 \times 10^{-6} \)[/tex] [tex]\( \frac{kg \cdot m}{s} \)[/tex].
So, [tex]\( 38.2 \frac{g \cdot dm}{hr} \)[/tex] is equal to [tex]\( 1.06111 \times 10^{-6} \frac{kg \cdot m}{s} \)[/tex] (rounded to five decimal places if needed).
1. Convert grams to kilograms:
- We know that 1 gram (g) is equal to 0.001 kilograms (kg).
- Therefore, [tex]\( 38.2 \)[/tex] grams is equal to [tex]\( 38.2 \times 0.001 = 0.0382 \)[/tex] kilograms.
2. Convert decimeters to meters:
- We know that 1 decimeter (dm) is equal to 0.1 meters (m).
- Therefore, [tex]\( 38.2 \frac{g \cdot dm}{hr} \)[/tex] becomes [tex]\( 0.0382 \frac{kg \cdot dm}{hr} \)[/tex].
- Converting the decimeters to meters, we get [tex]\( 0.0382 \times 0.1 = 0.00382 \)[/tex] [tex]\( \frac{kg \cdot m}{hr} \)[/tex].
3. Convert hours to seconds:
- We know that 1 hour (hr) is equal to 3600 seconds (s).
- Therefore, [tex]\( 0.00382 \frac{kg \cdot m}{hr} \)[/tex] becomes [tex]\( 0.00382 \div 3600 = 1.0611111111111113 \times 10^{-6} \)[/tex] [tex]\( \frac{kg \cdot m}{s} \)[/tex].
So, [tex]\( 38.2 \frac{g \cdot dm}{hr} \)[/tex] is equal to [tex]\( 1.06111 \times 10^{-6} \frac{kg \cdot m}{s} \)[/tex] (rounded to five decimal places if needed).