1. Chapter 2: Measurement

2. Units of Measurement SI units Base unit
based on the International System of Units
Base unit
a defined unit based on an object or event in the physical world
Important Base Units to Know:
Time (second, s) Length (meter, m)
Mass (kilogram, kg) Volume (liter, L)
Temperature (Kelvin, K)
Density (grams/centimeter3, g/cm3)

3. Derived Units
Density and Volume are derived units meaning that they are combined units
Ex. The volume of a block of wood can be determined by finding L x W x H  therefore the units would be cm x cm x cm or cm3
Ex. Density is mass divided by volume or g/cm3

4. Prefixes (p. 26) Prefix Symbol Factor Scientific Notation Example Giga
109
gigameter (Gm)
Mega M
106
megagram (Mg)
Kilo k
1000
103
kilometer(km)
Deci d
1/10
10-1
deciliter (dL)
Centi c
1/100
10-2
centimeter (cm)
Milli m
1/1000
10-3
milligram (mg)
Micro 1/
10-6
microgram (µg)
Nano n 1/
10-9
nanometer (nm)
pico p 1/
10-12
picometer (pm)

5. DENSITY Density = mass volume
Regular objects  simply find the mass by using a balance and then find volume by measuring length, width, and height (plug and chug)
What about irregularly shaped objects?

6. Density of Irregularly shaped objects
Measure the mass by using a balance
How do you find volume?
WATER DISPLACEMENT METHOD
Fill a graduated cylinder with certain amount of water (30mL)
Slowly lower object into the graduated cylinder and measure the change in water level.
Ex. Suppose cylinder plus object has a volume of 32 mL
The change in volume is 2 mL therefore the volume of the object is 2 mL

7. Scientific Notation Expresses numbers as a multiple of two factors
A number between 1 and 10
A ten raised to a power or exponent
Ex x 103  5000

8. Calculations with Scientific Notation
Addition and Subtraction- exponents must be the same so you will rewrite the number and then perform operation
4x x103 = 4x x102 = 54 x 102 or 5.4 x 103
Multiplication- exponents do not have to equal instead perform operation on the factors and then add exponents
(3 x 102) x (4 x 105) = 12 x 107 or 1.2 x 10 8
Division- exponents do not have to be the same instead perform operation on the factors and then subtract exponents
(1.5 x 105) / (3x103)= 0.5x102 or 5x101

9. Accuracy in Measurement
You cannot be more accurate than the instrument in which you use to measure
Ex. A bathroom scale measures pounds to the 1/10. Will you ever be able to determine your weight to the 1/1000 with this particular scale? NO

10. Precision of Calculated Results
calculated results are never more reliable than the measurements they are built from
Multi-step calculations: never round intermediate results!
General rules on rounding:
If it ends in 4 or below, round down to nearest whole number
52.63  52.6
If it ends in 5 or up, round up to nearest whole number
52.67  52.7

11. Uncertainty in Measurements
Making a measurement involves comparison with a unit or a scale of units
It is important to read between the lines
the digit read between the lines is always uncertain
convention: read to 1/10 of the distance between the smallest scale divisions
Significant Figures
definition: all digits up to and including the first uncertain digit
the more significant digits, the more reproducible the measurement is.
counts and defined numbers are exact- they have no uncertain digits!

12. Rules for Significant Figures
1. All digits are significant except for zeros at the beginning of the number and possibly terminal zeros.
2. Terminal zeros to the right of the decimal point are significant
3. Terminal zeros in a number without an explicit decimal point may or may not be significant. If doubt, write in scientific notation and then do significant figures.
4. When multiplying or dividing, give as many significant figures in the answer as there are in the measurement with the least number of significant figures.
5. When adding or subtracting measured quantities, give the same number of decimal places in the answer as there are in the measurement with the least number of decimal places.

13. Examples of the Rules
Rule 1 example: cm, cm, and all have 3 sig fig
Rule 2 example: cm, cm, and cm all have 4 sig fig
Rule 3 example: 900cm could have 1, 2, or 3 sig fig. If it was 900., then it would be 3. So, write it in sci. notation 9.00x102; therefore, 3 sig fig.
Rule 4 example: 4.1 x 5. =20.5=2. x101
Rule 5 example: = 186.5

14. Conversions Between Units
Use Factor Label Method aka Dimensional Analysis
Must know relationships among units
These relationships are called conversion factors
Ex mm = 1 m

15. Common Factors 1km=1000m kilometers to meters
1hm=100m hectometers to meters
1dam=10m decameters to meters
1m=1 m base
1m=10dm meter to decimeter
1m=100cm meter to centimeter
1m=1000mm meter to millimeter
** substitute any metric base in place such as liter

16. Common Factors Tera = 1012 Symbol: T Giga = 109 Symbol: G
Mega = Symbol: M
Kilo = Symbol: k
Hecto = Symbol: h
Deca = Symbol: da
Deci = Symbol: d
Centi = Symbol: c
Milli = Symbol: m
Micro = Symbol: µ
Nano = Symbol: n
Pico = Symbol: p

17. How to Convert EXAMPLE: 4.5 m = _________hm
Xhm = 4.5 m x 1hm = hm or 4.5x10-2 hm
100m
225 cm =________ mm
Xmm = 225cm x 10 mm = 2250 mm or 2.25 x 103 mm
1 cm
Conversion factor is in red

18. Temperature Conversions
REMEMBER: Kelvin is SI base unit for temperature
Celsius  Kelvin
K= oC
Fahrenheit  Celsius
oF=(1.8 x oC) +32
Fahrenheit  Celsius  Kelvin