1. Metric Prefixes

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

3. 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)

4. 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

5. Metric Prefixes Larger than the base unit Giga (G) 1 x 109 m = 1 Gm
means 1,000,000,000
Mega (M) x 106 g = 1 Mg
means 1,000,000
Kilo (k) 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

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

7. Metric Prefixes Smaller than the base unit micro () 1 g = 1 x 106 g
means 1/1,000,000
nano (n) 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

8. 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

9. 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

10. 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

11. 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 g
1 kg

12. 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

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

14. Practice = 260,000mg How many milligrams are in 260 grams?
260 g x mg g
= 260,000mg

15. 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.

16. 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.

17. 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

18. 2 Step problem
Example – How many milligrams are in 3.42 kg? 2. Write down your known 3.42 kg

19. 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 g
1 kg

20. 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 g mg
1 kg 1g

21. 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 g mg
1 kg 1g
= x 106 mg

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

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

24. Practice
How many megameters are in 50 Angstroms?

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

26. English-Metric Conversions

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

28. 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

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

30. 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

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

32. 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 m cm in ft =
1 x 109 nm 1m cm in
= x 10-7 ft

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

34. Practice = 3.4 x 105 mg How many milligrams are in 12 ounces?
oz  lb  g  mg
12 oz lb g mg
16 oz lb g
= x 105 mg

36. Practice
How many miles are in 17.0 km?

37. 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 m 100cm in ft mi
1km m cm 12 in ft
= mi

39. Velocity Conversions

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

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

42. 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 min =
hr 1 km 60 min 60 s

43. 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 min =
hr 1 km 60 min 60 s
40.6 m/s

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