1. Metric conversions: table
prefix
abbr.
conversion factor (multiply by)
example
tera- T
1012= (a trillion)
1 TB (big hard drive)
giga- G
109= (a billion)
1.3 GW in “Back to the Future”
mega- M
106= (a million)
512 MB (decent video card memory)
kilo- k
103=1 000 (a thousand)
20 kt (Hiroshima atomic bomb TNT equivalent)
hecta- h
102=100 (a hundred)
0.5 ha (0.5 hectares – area of a football field)
deka- da
101=10 (a ten)
rarely used --
100=1 (a unit)
deci- d
10–1=0.1 (a tenth)
1 dm (width of a hand)
centi- c
10–2=0.01 (a hundredth)
50 cm (average newborn length)
milli- m
10–3=0.001 (a thousandth)
8 mm (width of a pencil)
micro- μ
10–6= (a millionth)
7 μm (size of a red blood cell)
nano- n
10–9= (a billionth)
2 nm (width of DNA molecule)
pico- p
10–12= (a trillionth)
1 ps laser (produces a 0.3 mm light pulse)

2. 4 ways to use metric conversions
Translate the prefix.
Smaller or larger unit?
Staircase or line.
Multiply by 1.

3. 1. Translate the prefix 1. Recognize that “km” means “kilometer(s)”.
Example: convert 5 km to meters.
1. Recognize that “km” means “kilometer(s)”.
2. Remember (look up) the meaning of “kilo-”: “1000” or a “thousand”.
3. Read “5 kilometers” as “5 thousand meters”.
4. Write it as a number: 5 km = 5000 m.
NOTE: if you need to solve opposite problem (from m to km), do the opposite operation (e.g. 5 g = 5/1000 kg = kg).

4. 2. Smaller or larger unit?
Example: convert 2 mL to liters.
1. Recognize that “mL” means “milliliter(s)”.
2. Remember (look up) the meaning of “milli-”: “1/1000” or “one thousandth”. So, mL is a smaller unit than L, and L is a larger unit than mL.
3. The same quantity measured in larger units is expressed with smaller number (e.g. 24 in = 2 ft). Therefore, to go from small units (mL) to large units (L), you must reduce the number. How much? See #1 – by 1000 times!
4. Write your answer: 2 mL = 2/1000 L = L.

5. 3. Metric conversions: staircaseMm
mega-
(million)
0.002 km
kilo-
(thousand)
2 m
meters
2000 mm
milli-
(thousandth) µm
micro-
(millionth)

6. 3. Metric conversions: line
factor of 100*1000=100000=105
50 mm
5 cm
0.05 m km
factor of 10
factor of 100
factor of 1000
factor of 10*100=1000
factor of 10*1000*1000=

7. 4. Multiply by 1 1. Recognize that “cm” means “centimeter(s)”.
Example: convert 180 cm to meters.
1. Recognize that “cm” means “centimeter(s)”.
2. Remember (look up) the meaning of “centi-”: “1/100” or “one hundredth”, so there are 100 cm in 1 m.
3. If you multiply your value by 1, you will not change it, right? Since 1 m = 100 cm, you can always write 1 = (1 m)/(1 m) = (1 m)/(100 cm).
4. Let’s do it (height of a man):
180 cm = 180 cm × 1 = 180 cm × 1 m / 100 cm =
= 180 cm × 1 m / 100 cm = (180/100) m = 1.8 m

8. 4. Multiply by 1
Example (height of a man): convert 180 cm to meters.