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Chapter 2: Measurements
and Calculations
Ch 2.1 Scientific Method
Steps to the Scientific Method
(1) Make observations-- Use your 5 senses to gather
information.
(2) Propose a hypothesis-- Make an “educated guess” for
what is happening.
(3) Perform experiments-- This tests your hypothesis.
Many experiments are sometimes needed to test a
hypothesis. The same experiment must give similar
results if the experiment is to be reliable.
(4) Make a theory-- This should explain the results of
your experiments. Theories may change or be rejected
over time because of results from new experiments.
 Models: are a part of theory that is an explanation of
how phenomena occur and how data or events are
related.
 Qualitative Data: non-numerical data (ex. Green car)
 Quantitative Data: numerical data (ex. 12 cars)
Ch 2.2 Measurement
Every measurement must have a unit.
Base Units
 There are 7 base
units in SI.
 A Base unit is a
defined unit in a
system of
measurement that is
based on an object
SI Base Units
Length (l)
Meter (m)
Mass (m)
Kilogram (kg)
Time (t)
Second (s)
Temperature (T)
Kelvin (K)
Celsius (°C)
Amount of
Substance (n)
Mole (mol)
Electric
Current (I)
Ampere (A)
Luminous
Intensity (Iv)
Candela (cd)
Metric System
 An easy way to move within the metric system is by
moving the decimal point one place for each “step”
desired
 Example: change meters to centimeters
 Use Prefixes!!!
Kilo
1000
Hecto
100
To convert to a smaller unit,
move decimal point to the right
or multiply.
Deka
10
To convert to a bigger unit,
move decimal point to the left
or divide.
Basic
Unit
Deci
10
Centi
100
Milli
1000
Metric System
 400000 centimeters = _________kilometers
 500 kilometers = __________meters
Kilo
1000
Hecto
100
To convert to a smaller unit,
move decimal point to the right
or multiply.
Deka
10
To convert to a bigger unit,
move decimal point to the left
or divide.
Basic
Unit
Deci
10
Centi
100
Milli
1000
Derived Units
 A unit that is defined by a combination of base units
is called a derived unit.
 Examples are Area, Volume, Density, Molar Mass,
Molar Volume, and Energy.
 The two derived units we will be working with in this
chapter are volume and density.
Volume
 Volume is the space occupied by an
object.
 The derived unit for volume is the cubic
centimeter (cm3); used for solid objects.
 Liters (L) are used to measure the
amount of liquid in a container.
 For the smaller quantities of liquids,
volume is measured in milliliters (mL).
 1 mL = 1 cm3
Density
 Density is a ratio that compares the mass of an
object to its volume
 The units for density:
 grams per cubic centimeter(g/cm3) for solids
 grams per milliliter (g/mL) for liquids
 The density of an object will determine if it will float
or sink in another phase. If an object floats, it is less
dense than the other substance. If it sinks, it is more
dense.
 The density of water is 1.0 g/ml.
Example 1
A sample of aluminum metal has a mass of
8.4 g. The volume of the sample is 3.1 cm3.
Calculate the density of aluminum.
Answer
2.7 g/cm3
• A conversion factor is a ratio of equivalent
values used to express the same quantity in
different units.
• A conversion factor is always equal to 1.
• Because a quantity does not change when it
is multiplied or divided by 1, conversion
factors change the units of a quantity without
changing its value.
• This is also known as dimensional analysis
and it will be used a lot throughout the year.
The key to doing dimensional analysis is
making sure that your units cancel out!
Example 2
 Express a mass of 5.712 grams in
milligrams and kilograms
 Grams to milligrams
1 g = 1000 mg
 Grams to kilograms
1 kg = 1000 g
Answer
5712 mg
0.005712 kg
Temperature
 The temperature of an object is a measure of how hot or cold the
object is relative to other objects.
 Temperature scales - scientists use two temperature scales
 Celsius (oC) scale was devised by Anders Celsius
 Freezing point of water – 0 oC
 Boiling point of water – 100 oC
 the Kelvin (K) scale was devised by William Thomson and is the
SI base unit of temperature
 On the Kelvin scale water freezes at 273 K and boils at 373 K
 °C + 273 = K
 K – 273 = °C
Example
Convert the following Celsius temperatures
to Kelvin.
A. 42oC
B. 100oC
C. 68oC
Ch 2.3 Using Scientific Measurements

A digit that must be estimated
is called uncertain. A measurement
always has some degree of
uncertainty.
Precision and Accuracy

Accuracy refers to the agreement of a particular
value with the true value.

Precision refers to the degree of agreement among
several measurements made in the same manner.
Neither
accurate nor
precise
Precise but not
accurate
Precise AND
accurate
Percent Error
 Experimental values are measured during an
experiment
 Accepted value = true value
 Error = (Experimental value - accepted value)
 When you calculate percent error, you ignore plus and
minus signs
 The lower the % error means lab technique is good.
Significant Figures
 Scientist indicate the precision of
measurements by the number of digits they
report - Significant figures or Sig Figs
 A value of 3.52 g is more precise than a value
of 3.5 g.
Rules for Counting Significant Figures in a Measurement
Here is how you count the number of sig. figs. in a given
measurement:
#1 (Non-Zero Rule): All digits 1-9 are significant.
3
2 S.F.
*Examples: 2.35 g =_____S.F.
2200 g = _____
#2 (Straddle Rule): Zeros between two sig. figs. are significant.
3
4
*Examples: 205 m =_____S.F.
80.04 m =_____S.F.
5
7070700 cm =_____S.F.
#3 (Righty-Righty Rule): Zeros to the right of a decimal point AND anywhere to
the right of a sig. fig. are significant.
3
*Examples: 2.30 sec. =_____S.F.
3
20.0 sec. =_____S.F.
4
0.003060 km =_____S.F.
Rules for Counting Significant Figures in a Measurement
#4 (Bar Rule): Any zeros that have a bar placed over them are sig.
(This will only be used for zeros that are not already significant
because of Rules 2 & 3.)
4
*Examples: 3,000,000 m/s =_____S.F.
2
20 lbs =____S.F.
#5 (Counting Rule): Any time the measurement is determined by
simply counting the number of objects, the value has an
infinite number of sig. figs. (This also includes any conversion
factor involving counting.)
∞
∞
*Examples: 15 students =_____S.F.
29 pencils = ____S.F.
∞
7 days/week =____S.F.
∞
60 sec/min =____S.F.
Sig Fig Practice #1
How many significant figures in each of the following?
1.0070 m 
17.10 kg 
100,890 L 
3.29 x 103 s 
5 sig figs
4 sig figs
5 sig figs
3 sig figs
0.0054 cm 
2 sig figs
3,200,000 
2 sig figs
Rules for Significant Figures in
Mathematical Operations

Addition and Subtraction: use the least
number of places after the decimal between all
the numbers you are adding or subtracting.
 6.8 + 11.934 =
 18.734  18.7 (3 sig figs)
Sig Fig Practice #2
Calculation
Calculator says:
Answer
10.24 m
10.2 m
76.27 g
76.3 g
0.02 cm + 2.371 cm
2.391 cm
2.39 cm
713.1 L - 3.872 L
709.228 L
709.2 L
3.24 m + 7.0 m
100.0 g - 23.73 g
Rules for Significant Figures in Mathematical
Operations

Multiplication and Division: use the least
number of sig figs between the numbers you are
measuring.
 6.38 x 2.0 =
 12.76  13 (2 sig figs)
Sig Fig Practice #3
Calculation
Calculator says:
Answer
3.24 m x 7.0 m
22.68 m2
100.0 g ÷ 23.7 cm3
4.219409283 g/cm3
0.02 cm x 2.371 cm
0.04742 cm2
0.05 cm2
236.6666667 m/s
240 m/s
710 m ÷ 3.0 s
23 m2
4.22 g/cm3
Scientific Notation
Cartoon courtesy of NearingZero.net
Scientific Notation
 Scientific notation is a way of representing really large
or small numbers using powers of 10.
*Examples: 5,203,000,000,000 miles = 5.203 x 1012 miles
0.000 000 042 mm = 4.2 x 10−8 mm
Steps for Writing Numbers in Scientific Notation
(1) Write down all the sig. figs.
(2) Put the decimal point between the first and second
digit.
(3) Write “x 10”
(4) Count how many places the decimal point has
moved from it’s original location. This will be the
exponent...either + or −.
(5) If the original # was greater than 1, the exponent
is +, and if the original # was less than 1, the
exponent is - ....(In other words, large numbers
have + exponents, and small numbers have exponents.)
Scientific Notation
•
Practice Problems: Write the following measurements in
scientific notation or back to their expanded form.
477,000,000 miles = _______________miles
4.77 x 108
9.10 x 10−4
0.000 910 m = _________________
m
6,310,000,000
6.31 x 109 miles = ___________________
miles
0.00000388
3.88 x 10−6 kg = __________________
kg
PERFORMING
CALCULATIONS
IN SCIENTIFIC
NOTATION
ADDITION AND SUBTRACTION
4 x 106
+ 3 x 106
6
7 x 10
IF the exponents are
the same, we simply
add the numbers in
front and bring the
exponent down
unchanged.
6
10
106
4x
-3x
1 x 106
The same holds
true for subtraction
in scientific
notation.
6
10
4.00 x
5
+ 3.00 x 10
If the
exponents are
NOT the same,
we must move
a decimal to
make them the
same.
6
10
6
10
4.00 x
4.00 x
6
5
.30 x 10
+ 3.00 x 10
6
4.30 x 10
+
Move the
decimal on
the smaller
number!
A Problem for you…
-6
10
2.37 x
-4
+ 3.48 x 10
Solution…
-6
002.37
2.37 x 10
-4
+ 3.48 x 10
Solution…
-4
0.0237 x 10
-4
+ 3.48 x 10
-4
3.5037 x 10
3.50 x
-4
10
MULTIPLYING AND DIVIDING
4.0 x
X 3.0 x
106
105
Multiply the front
factors first.
Then add the
exponents.
6
10
4.0 x
5
x 3.0 x 10
11
12.0x 10
=
1.2 x
Make sure that only one
number is in front of the
decimal at the end of the
problem.
12
10
Divide
the
front
4.0 x
factors
first.
5
÷ 3.0 x 10
Then subtract the
exponents.
106
6
10
4.0 x
5
÷ 3.0 x 10
1
1.3 x 10