Chapter 2: Measurement and Calculations
Key concepts:
 Differentiate between accuracy and precision
 Apply principles of measurement and significant figures
 Identify and use the 7 base SI units
 Name and apply units of measure
 Perform unit conversions
 Calculate density
 Calculate percent error

A. Accuracy vs. Precision
__________ - How close you are to the correct measurement or calculation based on the standard value.
__________ - How close your measurements are to
EACH OTHER
The density of aluminum is 2.78 g/cm 3 .
Bob calculates the density three times and gets 2.75, 2.79 and 2.77.
AVG: 2.77
ACCURATE AND PRECISE
Mary calculates the density three times and gets 4.66, 4.67, and 4.65
AVG: 4.66
PRECISE BUT NOT ACCURATE
Holden calculates the density three times and gets 10.25, 6.87, and 1.25
AVG: 6.12
NIETHER ACCURATE NOR PRECISE
Franz calculates the density three times and gets 2.90, 1.95, 3.44
AVG: 2.76
ACCURATE BUT NOT PRECISE

B. Measurement
Measurement amount.
Unit defined size.
Metric base 10.
SI that uses only BASE metric units

B. Measurement
Quantitative size.
Qualitative descriptions
Examples:
20 ml of water QUANTITATIVE
The reaction bubbles QUALITATIVE
Uma Thurman is blonde QUALITATIVE
17 g/ml
Bulldogs are #1
QUANTITATIVE
QUALITATIVE

C. Significant figures
Significant figures indicate the accuracy of the measuring instrument.
2.35 cm
Last digit is ESTIMATED
Not possible to estimate 2.3514584; can only estimate between graduations

C. Significant figures
Consider the following:
What’s the estimate?
This ruler isn’t as accurate as the previous.

C. Significant figures
RULE
All nonzero digits and zeros between those digits are significant
Leading zeros with decimal points are NOT significant;
Ending zeros ARE significant with decimal
Ending zeros left of the decimal point may or may not be significant.
Indication needed.
EXAMPLE NO. OF SIG FIGS
1 458 g
40.7 m
10 150.01 mm
0.0005 kg
0.01008 m
1 701.10 L
0.00140500 m
4
6
6
7
1
4
3
15 000 kg
15 000. kg
2
5
1.50E4 kg
1.500E4 kg
3
4
Scientific notation is always in sig fig form

C. Significant figures
ADDITION AND SUBTRACTION
Answer has as many DECIMAL POINTS as the part with the LEAST decimals.
5.44 – 2.6106 =
2.099 + 0.05681 =
2.4 – 15.82 =
0.258 + .1 =

C. Significant figures
MULTIPLICATION AND DIVISION
Answer can only contain as many SIG FIGS as the part with the LEAST sig figs
8.15 x 6 =
1.2 x 1010 =
0.250 / 0.87 =
17.05 / 1.50 =

C. Significant figures
How about this one: (not in your notes; use calc)
 20

D. SI base units
Quantity
Length
Mass
Time
Temperature
Amount of substance
E. Current
Luminous intensity
Scientific researchers use ONLY these units!
Unit
Meter
Kilogram
Second
Kelvin
Mole
Ampere candela
We won’t
Abb.
m kg s
K mol
A cd

D. SI Base units cont.
Derived units – Made up of the base units
Quantity
Area
SI Unit m 2
Other Units acres, cm 2 , ft 2
Volume
Density
Speed
Energy m 3 kg m 3 m s
2 s 2
L, gal, cm 3 g cm 3 slugs ft 3 mi/hr, ft/s
Calorie, kWhr

E. Unit Conversions – metric prefixes kilo hecto deca unit deci centi milli king hector Doesn't Usually Drink Chocolate milk
EXAMPLES
1 000g = ________ Kg
0.23 Kg =________ dg
0.043 dam = _______ mm
15.25 cL = ________ HL
345 DaL = _____ Km 101.34 Km = ___________ mm

F. Metric conversions – conversion factors
All conversions start with an EQUALITY
1 inch is the same as 2.54 cm
1 inch = 2.54 cm
Equalities are turned into conversion factors:
1inch
2.54cm
or
2.54cm
1inch
Notice the top and bottom are same length!

F. Metric conversions – conversion factors
Convert 34 inches to centimeters
34 in 


2.54
1 in cm


 
86.36 cm
Conversion factor goes here

F. Metric conversions – conversion factors
The Bulldogs need 550 cm for a first down. How many yards is that?
MULTI-
STEP
Plan: cm  inch  feet  yards
550 cm
1
2.54
in cm




1
12 ft in






1
3 yd ft 

 
6 yards

F. Metric conversions – conversion factors
A baseball is thrown 60 ft/s. How fast is this in miles/hour?
Two things to convert.
1. ft  miles
2. s  min  hours
Do one at a time.
60 ft s
1 mi
5280 ft



60
1 s min






60
1 min hr 

 
40.91 mi/hr

F. Metric conversions – powered units
Misconception: 1 m = 100 cm but
1m 3 ≠ 100 cm 3
1 m 3 cube
1 m
100 cm
1 m
100 cm
1 m
100 cm
So, 100x100x100 =
1,000,000 cm 3
If the unit is cubed, you cube the numbers too
(1 m) 3 = (100 cm) 3
1 m 3 = 1,000,000 cm 3

F. Metric conversions – Volumes
Critical equality:
1 ml = 1 cm 3
How many liters of fuel does a 300 m 3 tank hold?
300 m 3
1,000,000
1 cm 3 m 3
1
1 ml cm 3
1
1,000
L ml
 

300,000 L
Or you could do King Hector

F. Metric conversions - Temperature
180 F o = ? K
Work:
F o  9
5
C o  32
 C o 
F o  32

9 o
5
C 82.2
o
F
 o  o
9
5
 o  273

C
273 o  32

G. Density
Measure of how tightly packed matter is.
More dense

Floating Boat on SF
6

Inhaling SF
6

G. Density, cont.
D  mass
 m volume V
Units: g cm 3 or g ml
When measuring
LxWxH
When measuring
Volume w/ cylinder

G. Density, cont.
A liquid has a density of 0.87 g/mL. What volume is occupied by 25 g of the liquid?
Given:
D = 0.87 g/mL
V = ?
M = 25 g
V
Work:
 m
D
V 
25g
.87g/ml
D  m
V 
V 28.74ml
V 29ml(sigfigs)

H. Percent Error
%E 

V a e
%E = Percent error
V a
= Accepted value
V e
= Experimental value
Example:
A student measures the density of a solid as
3.42 g/cc. The solid really has a density of 3.76 g/cc. Calculate the percent error. cc = cubic centimeter
V a
= 3.76 g/cc V e
= 3.42 g/cc

H. Percent Error, cont
Given:
V a
V e
= 3.76 g/cc
= 3.42 g/cc
%E 

V a e
Watch parentheses here!!!
Work:
%E 
3.76
%E = 0.09042
%E = 9.04% (sig figs)
You can ignore negative signs. A positive percent means the accepted value is higher than your value. A negative means it’s lower.