show that 1mg/L = 1g/m3
1 mg/L = 1 g/m^3.
1m = 100 cm
1m^3 = 100 cm x 100 cm x 100 cm = 1,000,000 cc and 1,000,000 cc = 1,000L.
Therefore, 1 m^3 = 1E6 cc
1 gram = 1000 mg; thus, 1 mg/L = 1000 mg/1,000,000 cc. Divide numerator and denominator by 1000 to arrive at 1 mg/1000 cc which is 1 mg/L. I did it backwards; I guess that's ok.
To show that 1 milligram per liter (mg/L) is equal to 1 gram per cubic meter (g/m^3), we can use the conversion factors between the metric units.
1 milligram (mg) is equal to 0.001 grams (g), and 1 liter (L) is equal to 0.001 cubic meters (m^3).
So, to convert from mg/L to g/m^3, we can multiply 1 mg/L by the equivalent factors:
(1 mg/L) x (0.001 g/1 mg) x (0.001 m^3/1 L) = (1 * 0.001 *0.001) (g * m^3) / (1 * 1 *1) (mg * L)
Simplifying the expression, we get:
0.001 * 0.001 = 0.000001
Therefore, 1 mg/L is equal to 0.000001 g/m^3.
To show that 1 milligram per liter (mg/L) is equal to 1 gram per cubic meter (g/m³), we need to convert the units.
We know that:
1 milligram (mg) = 0.001 grams (g)
1 liter (L) = 0.001 cubic meters (m³)
Now, let's convert 1 mg/L to g/m³:
1 mg/L = 0.001 grams/0.001 cubic meters
Canceling out the common units:
1 mg/L = 1 gram/1 cubic meter
Therefore, we have shown that 1 mg/L is equal to 1 g/m³.