Must have a number and a UNIT
 SI measurements

Base units are
defined units
based on an
object or event
in the physical
world.
Base units are
independent of
other units.


A unit that is defined by a combination of base
units is called a derived unit.
Volume
› space occupied by an object
› Cubic meter (m3)

Density
› Ratio that compares the mass of an object to its
volume
› Density = mass / volume
› Grams/cubic centimeter (g/cm3)

Speed
› distance / time (meters/second)


Temperature is a measure of how
hot or cold a substance is relative
to other objects
Kelvin scale (no degrees used)
› Water boils at 373 K
› Water freezes at 273 K

Celsius scale
› Water boils at 100oC
› Water freezes at 0oC

Converting
› oCelsius to Kelvin – oC + 273
› Kelvin to oCelsius –Kelvin - 273
› oCelsius to oFahrenheit – 5/9 (oF -32)
› oFahrenheit to oCelsius – 9/5 (oC +32)
The Problem
1. Read the problem
2. Be sure that you understand what it is asking you.
Analyze the Problem
1. Read the problem
2. Identify what you are given and list the known data
3. Identify and list the unknown
4. Gather information you need from graphs, tables, or figures
5. Plan the steps you will follow to find the answer
Solve for the unknown
1. Determine whether you need a sketch to solve the problem.
2. If the solution is mathematical, write the equation and isolate the
unknown factor
3. Substitute the known quantities into the equation
4. Solve the equation
5. Continue the solution process until you solve the problem
Evaluate the Answer
1. Re-read the problem. Is the answer reasonable?
2. Check your math. Are the units and the
significant figures correct?
Expresses numbers as a multiple of two
factors
 First factor must follow this rule
1 ≤ 1st factor < 10
 When numbers larger than 1 are
expressed in scientific notation, the power
of ten is positive
 When numbers smaller than 1 are
expressed in scientific notation, the power
of ten is negative



Express the following in scientific notation
a.
700 m
e.
0.0054 kg
b.
38,000 m
f.
0.00000687 kg
c.
4,500,000 m
g.
0.000000076 kg
d.
685,000,000,000 m
h.
0.0000000008 kg
Express the following quantities in
scientific notation
i.
360,000 s
j.
0.000054 s
k.
5060 s
l.
89,000,000,000 s




Exponents must be the same
If they are not the same change the quantities so that
the exponents are the same
› Move decimal to the left – increase the exponent
value
› Move decimal to the right – decrease the exponent
value
› Left
› Add
› Right
› Subtract
Add or subtract the number values
Exponents will be the same as the original values

Multiplication
› Exponents do not
have to be the
same
› Multiply the first
factors
› Then add the
exponents

Division
› Exponents do not
have to be the
same
› Divide the first
factors
› Then subtract the
exponent of the
divisor from the
exponent of the
dividend
Take care when determining the sign of the exponent.

Conversion Factor
› A ratio of equivalent values used to express the
same quantity in different units
› A conversion factor is always equal to 1
› Change the units without changing the value

Dimensional Analysis
› Method of problem solving that focuses on the
units used to describe matter
› Converting from large unit to a small unit the
number of units must increase
a.
Convert 360 s to ms
e.
Convert 245 ms to s
b.
Convert 4800 g to kg
f.
Convert 5 m to cm
c.
Convert 5600 dm to m
g.
Convert 6800 cm to m
d.
Convert 72 g to mg
h.
Convert 25 kg to Mg
How many seconds are there in 24
hours?
 The density of gold is 19.3 g/mL. What is
gold’s density in decigrams per liter?
 A car is traveling 90.0 km/hr. What is its
speed in miles per minute? 1 km = 0.62
miles

24 hr
60 min
60 sec
1 hr
1 min
19.3 g
10 dg
1000 mL
mL
1g
1L
90.0 km
hr
0.62 miles
1 hr
1 km
60 min
=
=
86,400 sec
193000
dg
L
=
0.930 miles
min
Accuracy refers to how close a
measured value is to an accepted value
 Precision refers to how close a series of
measurements are to one another

To evaluate the accuracy of
experimental data (recorded during
experimentation) you can calculate the
difference between an experimental
value and an accepted value
 The difference is called an error
 Percent error is the ratio of an error to an
accepted value.
 Percent Error =
error
x 100
accepted value

Doesn’t matter whether the
experimental value is larger or smaller
than the accepted value just how far off
it was
 Ignore the plus or minus sign
 Tolerances – narrow range of error that is
acceptable

Calculate the percent errors for Student B’s trials. (The accepted value is
1.59 g/cm3).
Calculate the percent errors for Student C’s trials. (The accepted value
is 1.59 g/cm3).
Scientists indicate the precision of
measurements by the number of digits
they report.
 The digits that are reported are called
significant figures
 Include all known digits and one
estimated digit.

Non-zero numbers are always significant
Zeros between non-zero numbers are
always significant
 All final zeros to the right of the decimal
place are significant
 Zeros that act as placeholders are not
significant. Convert quantities to scientific
notation to remove the placeholder zeros
 Counting numbers and defined constants
have an infinite number of significant
figures.











Determine the number of significant figures
in each measurement
508.0 L –
820400.0 L –
1.0200 x 105 kg –
807000 kg –
0.049450 s –
0.000482 mL –
3.1587 x 10-8 g –
0.0084 mL –
Calculators often give more significant
figures than are appropriate for a given
calculation
 Your answer should have no more
significant figures than the data with the
fewest significant figures





If the digit to the immediate right of the last significant
figure is less than five, do not change the last
significant figure
If the digit to the immediate right of the last significant
figure is greater than five, round up the last significant
figure
If the digit to the immediate right of the last significant
figure is equal to five and is followed by a nonzero
digit, round up the last significant figure
If the digit to the immediate right of the last significant
figure is equal to five and is not followed by a nonzero
digit, look at the last significant figure. If the last
significant figure is an odd digit, round it up. If the last
significant figure is an even digit do not round up
When adding or subtracting, your answer
must have the same number of digits to
the right of the decimal point as the
value with the fewest digits to the right of
the decimal point
 Round the answer to the same number
of places as the fewest in the equation
 Maintains the same precision as the least
precise measurement


When multiplying or dividing your answer
must have the same number of
significant figures as the measurement
with the fewest significant figures
Creating a graph can help scientists
reveal patterns among the data
gathered through experimentation
 We will deal with circle, bar and line
graphs

Also called pie chart
 Shows parts of fixed
whole
 Parts are usually
percentages

Bar graphs show how a quantity varies
with factors such as time, location, or
temperature
 The independent variable is plotted on
the horizontal (x-axis)
 The quantity being measured is plotted
on the vertical (y-axis) – dependent
variable
 Can also be used to compare data


Independent variable is plotted on the x-axis
› Variable scientist deliberately changes in the
experiment



Dependent variable is plotted on the y-axis
When points are scattered on the graph a line
of best fit must be drawn where an equal
number of data points fall above and below
the line of best fit
If the line of best fit is straight the variables are
directly related
› The relationship can be described by the slope of the
line

Line rises to the right = positive slope
› Dependent variable increases as the
independent variable increases

Line sinks to the right = negative slope
› The dependent variable decreases as the
independent variable increases
Slope is Constant
 Slope = y2 – y1 = ∆y
x2 – x1 ∆x


Interpolate
› Reading data from a graph that falls
between measured points

Extrapolate
› Extend the line beyond the plotted points
and estimate values for the variables