Metric Prefixes

Objectives Understand how to use the metric system to measure in science. Understand how to convert units. Understand why we need to convert units.

SI Units Base Units Time – second (s) Length – meter (m) Mass – gram (g) Volume – Liter (L) Temperature – Kelvin (K) Amount of a substance – mole (mol) Electric Current – ampere (A) Luminous intensity – candela (cd)

SI Units Derived Units (define) Volume – cubic decimeter (dm3) or liter (L) Density – kilograms/Liters (kg/L) Speed – meters/second (m/s) There are many more derived units

Metric Prefixes Larger than the base unit Giga (G) 1 x 109 m = 1 Gm means 1,000,000,000 Mega (M) 1 x 106 g = 1 Mg means 1,000,000 Kilo (k) 1 x 103 L = 1 kL means 1,000 Hecto (h) 1 x 102 m = 1 hm means 100 Deca (da) 1 x 101 g = 1 dag means 10

Metric Prefixes Smaller than the base unit deci (d) 1 g = 1 x 101 dg means 1/10 centi (c) 1 L = 1 x 102 cL means 1/100 milli (m) 1 m = 1 x 103 mm means 1/1,000

Metric Prefixes Smaller than the base unit micro () 1 g = 1 x 106 g means 1/1,000,000 nano (n) 1 L = 1 x 109 nL means 1/1,000,000,000 Angstrom (Å) 1 m = 1 x 1010 Å means 1/10,000,000,000

Conversion Fractions A fraction Will always have the base unit in the fraction (meter, liter, or gram) Will always have the number “1” with the larger valued prefix Fraction can be “flipped” depending on which unit you are trying to “factor” out and cancel

Dimensional Analysis or the Factor Label Method 1 step problem Example – How many grams are in 3.42 kg? Write down your known 3.42 kg

1 Step Problem kg Example – How many grams are in 3.42 kg? Write down the conversion that involves your known unit on bottom and the unit you want to go to on top. 3.42 kg x ______g kg

1 Step Problem 1 kg Example – How many grams are in 3.42 kg? 3. Give the larger prefix value a “one” 4. The other gets the value of the prefix. 3.42 kg 1000 g 1 kg

1 Step Problem 1 kg 5. Cancel out units and solve. Remember if you have the same unit on top and on bottom, they cancel out. 3.42 kg x 1000 g =3420 g 1 kg

Practice = 1.5 x 10-3 L How many Liters are in 1.5 x 106 nL? 1.5 x 106 nL 1L 1 x 109 nL = 1.5 x 10-3 L

Practice = 260,000mg How many milligrams are in 260 grams? 260 g x 1000 mg 1g = 260,000mg

Mystery of Orbiter Crash Solved By Kathy Sawyer Washington Post Staff Writer Friday, October 1, 1999; Page A1 NASA's Mars Climate Orbiter was lost in space last week because engineers failed to make a simple conversion from English units to metric, an embarrassing lapse that sent the $125 million craft fatally close to the Martian surface, investigators said yesterday. Officials are scrambling to determine whether a similar error is buried in the computer files of two other spacecraft currently cruising through space: the Mars Polar Lander, scheduled to hit the Martian surface on Dec. 3, and the Stardust craft bound for a comet.

It now appears the error had affected the orbiter mission from its launching almost 10 months and 416 million miles before its Sept. 23 failure. And yet the problem was never caught and corrected by the system of checks and balances at the Jet Propulsion Laboratory (JPL) in California, which manages this and numerous other interplanetary missions for NASA.

2 Step problem Start base final Example – How many milligrams are in 3.42 kg? Map out your strategy . Write the unit you are starting with, the base unit you are going to, and the unit you want to end with. kg  g  mg Start base final

2 Step problem Example – How many milligrams are in 3.42 kg? 2. Write down your known 3.42 kg

2 Step Problem Write down the first conversion. Remember, the conversion that involves your known unit on bottom and the base unit on top. 3.42 kg 1000 g 1 kg

2 Step Problem 4. Add the second conversion. Remember, the conversion that involves your base unit on bottom and the unit you want to go to on top. 3.42 kg 1000 g 1000 mg 1 kg 1g

2 Step Problem 1 kg 1g = 3.42 x 106 mg 5. Cancel out units and solve. Remember if you have the same unit on top and on bottom, they cancel out. 3.42 kg 1000 g 1000 mg 1 kg 1g = 3.42 x 106 mg

Practice How many milligrams are in 260 kilograms? kg  g  mg

Practice = 2.6 x 108 mg How many milligrams are in 260 kilograms? kg  g  mg 260 kg 1000 g 1000 mg 1kg 1 g = 2.6 x 108 mg

Practice How many megameters are in 50 Angstroms?

Practice = 5 x 10-15 Mm How many megameters are in 50 Angstroms? Å  m  Mm 50 Å 1m 1Mm 1 x 1010Å 1 x 106m = 5 x 10-15 Mm

English-Metric Conversions

English to Metric Conversions Length 2.54 cm = 1 in Mass 454 g = 1 lb Volume 1 L = 1.06 qt

Multiple Step problem Start base bridge finish Some English to Metric Calculations will have multiple steps. Ex. How many ft are in 240 nm? Map out your strategy . Write the unit you are starting with, the bridge between the two systems, and the unit you want to end with. nm  m  cm  in  ft Start base bridge finish

Multiple Step problem Example – How many ft are in 240 nm? Write down your known 240 nm

Multiple Step Problem 1 x 109 nm Write down the first conversion. Remember, the conversion that involves your known unit on bottom and the base unit on top. 240 nm 1 m 1 x 109 nm

Multiple Step Problem 240 nm 1m 100 cm 1 in 1 ft = Add the other conversions. 240 nm 1m 100 cm 1 in 1 ft = 1 x 109 nm 1m 2.54 cm 12 in

Multiple Step Problem = 7.9 x 10-7 ft 4. Cancel out units and solve. Remember if you have the same unit on top and on bottom, they cancel out. 240 nm 1 m 100 cm 1 in 1 ft = 1 x 109 nm 1m 2.54 cm 12 in = 7.9 x 10-7 ft

Practice How many milligrams are in 12 ounces? oz  lb  g  mg

Practice = 3.4 x 105 mg How many milligrams are in 12 ounces? oz  lb  g  mg 12 oz 1 lb 454 g 1000mg 16 oz 1 lb 1g = 3.4 x 105 mg

Practice How many miles are in 17.0 km?

Practice = 10.6 mi 17.0 km 1000 m 100cm 1in 1 ft 1 mi How many miles are in 17.0 km? km  m  cm  in  ft  mi 17.0 km 1000 m 100cm 1in 1 ft 1 mi 1km 1 m 2.54 cm 12 in 5280 ft = 10.6 mi

Velocity Conversions

Velocity Conversions Example – Ex. Convert 146 km/h to m/s. Write down your known 146 km h

Velocity Conversions h 1 km Write down the conversions for the top unit. 146 km 1 x 103 m h 1 km

Velocity Conversions 146 km 1 x 103 m 1 hr 1 min = hr 1 km 60 min 60 s Add the conversions for the bottom unit. 146 km 1 x 103 m 1 hr 1 min = hr 1 km 60 min 60 s

Velocity Conversions 40.6 m/s 146 km 1 x 103 m 1 hr 1 min = 4. Cancel out units and solve. Remember if you have the same unit on top and on bottom, they cancel out. 146 km 1 x 103 m 1 hr 1 min = hr 1 km 60 min 60 s 40.6 m/s

Practice How many yards per minute are in 52.6 hm/s?