Question

Calculate (to three significant figures) the numerical part of the conversion factors needed to carry out the following unit conversions:

a. density in g/cm3 to kg/m3
b. speed in mi/h to ft/s
c. area in km2 to mi2
d. area in km2 to cm2
e. mass/area of aluminum foil in mg/cm2 to g/m2
f. number of gas molecules per unit volume from /m3 to /ft3
g. number of bacteria per unit area on a microscope slide from /mm2 to /iN₂

Answer 1

To convert density from g/cm3 to kg/m3, multiply the original density value by 1000 to get the required conversion factor in kg/m3.

Step-by-step explanation:

To convert density from g/cm3 to kg/m3, you need to account for the conversion from grams to kilograms and from cubic centimeters to cubic meters. Knowing that 1 kg = 1000 g and 1 m3 = 106 cm3, we can derive the conversion factor by multiplying the original density by 1000 to convert grams to kilograms and then by one million to convert cubic centimeters to cubic meters, effectively multiplying the density value by 1000.

For example, if the density of a substance is 2.7 g/cm3 the conversion to kg/m3 would be 2.7 g/cm3 × 1000 kg/g × 1/106 m3/cm3 = 2700 kg/m3.