Metric conversions: table

1. Metric conversions: table

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 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 = 0.005 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 = 0.002 L.

5. 3. Metric conversions: staircase 0.000002 Mm mega- (million) 0.002 km kilo- (thousand) 2 m meters 2000 mm milli- (thousandth) 2000000 µm micro- (millionth)

6. 3. Metric conversions: line factor of 100*1000=100000=105 5 cm 0.00005 km 50 mm 0.05 m factor of 10 factor of 100 factor of 1000 factor of 10*100=1000 factor of 10*1000*1000=10000000

7. 4. Multiply by 1 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.