Conversion Process
including metric prefix conversions and other conversions with conversion factors
Metric Prefixes You Should Know
1 meter = 1,000,000 µm
1,000 mm
100 cm
10 dm
0.001 km
micrometers
millimeters
centimeters
decimeters
kilometers
(1 km = 1000 m)
Substitute any base unit for meter. What unit does each of the following represent?
ms =
____________________________
kg =
____________________________
mL =
____________________________
Converting between metric prefixes
Make a fraction of the values above with what you are converting to on top and from on bottom.
For example, to convert from 24500 mL to kL…
(24500 mL)
0.001 kL = ______________ kL Cancel out the mL units and you have kL!
1000 mL
Canceling out units in this way is known as dimensional analysis, and is a powerful tool for making sure you
are following a correct process.
Other conversions with Conversion Factors
Make a fraction of the conversion factor with what you are converting to on top and from on bottom.
For example, to convert from 345 calories to Joules, given 1 cal = 4.184 J…
(345 cal) 4.184 J
1 cal
= ______________J Cancel out the cal units and you have J!
Multistep Conversions
Use a series of fractions so that the units cancel out to form the desired unit.
For example convert from 53.0 yards to centimeters given 1 yd = 3 ft, 1 ft = 12 in, and 1 in = 2.54 cm…
(53.0 yd) 3 ft
1 yd
12 in
1 ft
2.54 cm
1 in
= ______________ cm
Dimensional analysis gives you cm!
Temperature Conversions
To convert from Celsius to Kelvins add 273. To convert from Kelvins to Celsius subtract 273.
For example convert 39 ºC to K…
39 ºC + 273 = 312 K
Conversion Practice. Show all set-ups and demonstrate dimensional analysis.
1. Convert 2.60 x 104 J to cal.
2. Convert 420 K to Celsius.
3. Convert 550 Calories (in a Big Mac) to J. (1 Cal = 1000 cal by definition)
4. Convert 0.0034 dJ to Cal.
5. Gold has a density of 19.31 g/mL. This provides a conversion factor 19.31 g = 1 mL
Find the volume in mL of 1.24 µg of gold. (Start with the DATA).
Start at the beginning again and find the volume in L,
6. Convert 25 °C to Kelvins.
7. Convert 4500 K to Celsius.
8. Convert 0.0023 cal to mJ.
9. 1 kg = 2.2 lbs. Convert 3.215 x 108 µg to lbs.
10. 1 cup = 946 cm3. Find the mass in kg of 2.5 cups of gold. (1 mL = 1 cm3, so gold’s density is 19.31 g/cm3)