1. Dimensional Analysis CONVERTING UNITS

2. The Fundamental SI Units (ie: Système International, SI)
Physical Quantity
Name
Abbreviation
Mass
kilogram kg
Length
meter m
Time
second s
Temperature
Kelvin K
Amount of Substance
(1 mol = 6.02x1023)
mole
mol

3. BASE UNIT SI Prefix Abbr Exp Meaning Equality mega M 106 kilo k 103
1 million x larger
1,000,000 base unit = 1 M_
kilo k
103
1,000 times larger
1,000 base unit = 1 k_
deca da 10
10 times larger
10 base unit = 1 D_
BASE UNIT
(meters, grams, liters, etc.) 1
1 base unit
deci d
10-1
1/10
1 base unit = 10 d_
centi c
10-2
1/100
1 base unit = 100 c_
milli m
10-3
1/1,000
1 base unit = 1,000 m_
micro 
10-6
1/million
1 base unit =
1,000,000 _
nano n
10-9
1/billion
1,000,000,000 n_
pico p
10-12
1/trillion
1,000,000,000,000 p_

4. Y Z E P T G M k h da d c m µ n p f a z y
FACTOR
...or in full ...
or in words
SI PREFIX
SI SYMBOL
1,0E+24 1,0E+21 1,0E+18 1,0E+15 1,0E+12 1,0E+9 1,0E+6 1,0E+3 1,0E+2 1,0E+1 1,0E-1 1,0E-2 1,0E-3 1,0E-6 1,0E-9 1,0E-12 1,0E-15 1,0E-18 1,0E-21 1,0E-24
,1 0,01 0,001 0, , , , , , ,
septillion sextillion quintillion quadrillion trillion billion million thousand hundred ten tenth hundredth thousandth millionth billionth trillionth quadrillionth quintillionth sextillionth septillionth
yotta- zetta- exa- peta- tera- giga- mega- kilo- hecto- deca- deci- centi- milli- micro- nano- pico- femto- atto- zepto- yocto-
Y Z E P T G M k h da d c m µ n p f a z y

5. SI Basic Units & Quantities
Length = meter (m)
Volume =
volume of 1m x 1m x 1m cube = 1 m3
More convenient = liter (L)
1 cm3 = 1 mL
10 drops H2O ≈ 1 mL
Mass = kilogram (kg)
Defined as the mass of 1 L of 4ºC
weight is a force that measures the pull on a given mass by gravity

6. SI Basic Units & Quantities
Temperature =
Celsius (°C) -
Water 0 °C
Water 100 °C
Kelvin (K) - the absolute scale
Don’t use the degree symbol
Water 273 K
Water 373 K
K = °C + 273
°C = K - 273

7. Conversion Factors Quantities can be expressed several different ways
1 dollar = 4 quarters = 10 dimes = 20 nickels = 100 pennies
1 meter = 10 decimeters = 100 centimeters = 1000 millimeters
Conversion Factor: a ratio of equivalent measurements
Units are vital
Numerator and denominator are equivalent
Conversion factors change the number & unit, however, the actual size of the quantity measured remains the same.

8. Conversion Factors Examples: 1 dollar = 100 pennies 1 dollar
1 L = 1,000 mL
1 L
1,000 mL OR
1,000 mL
1 L

9. Conversion Factors Smaller # Larger Unit 1 dollar 100 pennies Larger #
Smaller Unit
How many significant figures does a conversion factor within a system of measurement have?
Unlimited

10. Dimensional Analysis 60 min 1 h 60 sec 1 min 8 h x x = 28,800 s
Set up conversion factors so that the units will cancel out to get to the desired unit
Cancel units & check for correct units
Multiply by numbers on the top
Divide by numbers on the bottom

11. Dimensional Analysis
A way to analyze and solve problems using units, or dimensions, of the measurements.
How many seconds are in a workday that lasts exactly eight hours?
Unknowns
Knowns
Plan
Solve

12. Dimensional Analysis
How many seconds are in a workday that lasts exactly eight hours?
Unknowns
8 hours = ? seconds
Knowns
time worked = 8 hours
1 hour = 60 minutes
1 minute = 60 secondsseconds
Plan - use the units
Solve

13. Dimensional Analysis 60 min 1 h 60 sec 1 min 8 h x x = 28,800 s
Set up conversion factors so that the units will cancel out to get to the desired unit
Cancel units & check for correct units
Multiply by numbers on the top
Divide by numbers on the bottom

14. Converting meters to centimeters
135 meters is how many centimeters?
Unknown= ? cm = 135 meters
Known: 1 meter = 100 cm
Plan: m  cm
Solve: m x cm = m
** Multiple top values, divide bottom values.
13, 500 cm

15. Converting meters to centimeters
233 centimeters is how many meters?
Unknown= ? m = 233 centimeters
Known: 1 meter = 100 cm
Plan: cm  m
Solve: cm x m =
100cm
** Multiple top values, divide bottom values.
2.33 m

16. Converting meters to centimeters
233 centimeters is how many millimeters?
Unknown= ? mm = 233 centimeters
Known: 1 centimeter = 10 mm
Plan: cm  mm
Solve: cm x mm =
1 cm
** Multiple top values, divide bottom values.
2330 mm

17. Converting meters to centimeters
3456 millimeters is how many centimeters?
Unknown= ? cm = 3456 millimeters
Known: 1 centimeter = 10 mm
Plan: mm  cm
Solve: mm x cm =
10mm
** Multiple top values, divide bottom values.
345.6 cm

18. Convert the Following
99.2 cm to meters
Unknown:
Known:
Plan:
Solve:

19. Convert the Following
2.34 m to cm
Unknown:
Known:
Plan:
Solve:

20. Convert the Following
2340 mm to cm
Unknown:
Known:
Plan:
Solve:

21. How many eggs do YOU weigh?
What is your unknown?
What do you know?
What is your plan?
Solve the problem!! ? =
5 dozen eggs weigh 2.5 kg

22. How many eggs do YOU weigh?=
What is your unknown?
What do you know?
What is your plan?
Solve the problem!!
5 dozen eggs weigh 2.5 kg

23. Convert the Following
How many minutes are there in exactly one week?

24. Convert the Following
How many seconds are in exactly a 40-hour work week?

25. Convert the Following
0.044 km to meters

26. Convert the Following
15 cm3 to liters

27. Convert the Following
The radius of a potassium atom is nm. Express this radius in the unit centimeters.

28. Convert the Following
The diameter of the Earth is 1.3 x 104 km. What is the diameter expressed in decimeters?

29. U: K: P: S:

30. Convert the Following
The mass of a unit volume of a substance is a property called density. The density of manganese is 7.21 g/cm3. What is the density of manganese expressed in units kg/m3?

31. Convert the Following
Gold has a density of 19.3 g/cm3. What is the density in kilograms per cubic meter?