Metric conversions: tableprefix abbr. conversion factor (multiply by) example

tera- T 1012=1 000 000 000 000 (a trillion) 1 TB (big hard drive)

giga- G 109=1 000 000 000 (a billion) 1.3 GW in “Back to the Future”

mega- M 106=1 000 000 (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=0.000 001 (a millionth) 7 μm (size of a red blood cell)

nano- n 10–9=0.000 000 001 (a billionth) 2 nm (width of DNA molecule)

pico- p 10–12=0.000 000 000 001 (a trillionth) 1 ps laser (produces a 0.3 mm light pulse)

4 ways to use metric conversions

1. Translate the prefix.2. Smaller or larger unit?3. Staircase or line.4. Multiply by 1.

1. Translate the prefixExample: 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 = 0.005 kg).

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 = 0.002 L.

3. Metric conversions: staircase

2 m

2000 mm

milli-(thousandth)

0.002 km

kilo-(thousand)

meters

mega-(million)

micro-(millionth)

0.000002 Mm

2000000 µm

3. Metric conversions: line

5 cm50 mm 0.05 m 0.00005 km

factor of 100*1000=100000=105

factor of 100 factor of 1000factor of 10

factor of 10*100=1000

factor of 10*1000*1000=10000000

4. Multiply by 1Example: 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

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

180 cm = 180 cm⋅1 =

180 cm⋅ 1m100 cm

=

180 cm⋅1m

100 cm=

1.8m