Transcript What is Scientific Notation?

Important Math Skills
for
Science
Learning Objectives
1.
Know and be able identify and use the standard SI
measurements for length, volume, mass, time, and
temperature.
2.
Be able to construct and use tables to present data.
3.
Be able to properly construct and interpret graphs.
4.
Distinguish whether data are accurate and/or precise.
5.
Know and apply rules for determining significant figures.
6.
Know and apply
calculations.
7.
Determine the percent of error in calculations.
8.
Distinguish between weight and mass.
rules
for
rounding
the
results
of
Types of Observations and
Measurements
observations —
changes in color and physical state.
 QUANTITATIVE MEASUREMENTS,
which involve numbers.
 Use SI units — based on the
metric system
 QUALITATIVE
Standards of Measurement
When we measure, we use a measuring tool
to compare some dimension of an object to
a standard.
For example, at one time the
standard for length was the king’s
foot. What are some problems with
this standard?
Metric System (SI)



Is a decimal system based on 10
Used in most of the world
Used by scientists and hospitals
Units in the Metric System

length
meter
m

volume
liter
L

mass
gram
g

temperature
Celsius °C
Kelvin
°K
Stating a Measurement
In every measurement there is a
Number
followed by a
 Unit from measuring device
Key Concepts
Key Concepts
 Accuracy vs. Precision
Key Concepts
 Accuracy vs. Precision
 Significant Figures
Key Concepts
 Accuracy vs. Precision
 Significant Figures
 Rounding
Key Concepts






Accuracy vs. Precision
Percent / Experimental Error
Significant Figures
Rounding
Mass vs. Weight
Graphing
Accuracy vs. Precision
Precision – the reproducibility of a result or
measurement.
Accuracy – how close a result or measurement
is to the actual value.
Your goal should be to achieve both accuracy
and precision in your experimental results and
measurements.
Accuracy vs. Precision
Precise
Neither
accurate
nor
Precise
Accurate
and
Precise
How precise can you be?
Accurate? Precise?
The “true” value being measured is 45.25
Trial
1
Trial
2
Trial
3
45.50 39.99 32.05
44.35 39.60 19.44
45.01 40.01 37.75
44.67 38.95 38.33
All numeric data should be reported
with proper rounding and use of
significant figures.
Significant Figures
1. All non-zero digits are significant.
2. All leading and following zeros that are only
place-holders are not significant.
3. All zeros between
significant.
two
other
digits
are
4. All zeros to the right of the decimal and to the
right of other digits are significant. For instance,
the number 43.500 has five significant digits,
two of which are zeros. The number .0042 has 2
significant digits.
Significant Figures
5. Zeroes at the end of a number are significant
only if they are behind a decimal point.
Otherwise, it is impossible to tell if they are
significant. For example, in the number 8200, it
is not clear if the zeroes are significant or not.
The number of significant digits in 8200 is at
least two, but could be three or four. To avoid
uncertainty, use scientific notation to place
significant zeroes behind a decimal point:
8.200 X 103 has four significant digits
8.20 X 103 has three significant digits
8.2 X 103 has two significant digits
Rules for multiplying and dividing
The answer will have as many s.f. as the
least number of s.f. in the problem.
4.32 × .032 = .13824  .14
Rules for adding and subtracting.
The answer will have as many decimal
places as the least number of places to
the right of the decimal found in the
problem.
1.062
+6.8
7.862  7.9
4.26
+9.1
13.36  13.4
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

?
4087

?
23

?
.082

?
.00006

?
.000060

?
1.000060 
?
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

?
23

?
.082

?
.00006

?
.000060

?
1.000060 
?
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

?
.082

?
.00006

?
.000060

?
1.000060 
?
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

2
.082

?
.00006

?
.000060

?
1.000060 
?
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

2
.082

2
.00006

?
.000060

?
1.000060 
?
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

2
.082

2
.00006

1
.000060

?
1.000060 
?
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

2
.082

2
.00006

1
.000060

2
1.000060 
?
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

2
.082

2
.00006

1
.000060

2
1.000060 
7
1000.

?
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

2
.082

2
.00006

1
.000060

2
1.000060 
7
1000.

4
4000.00

?
 Check your understanding . . .
How many significant figures are in each of the following
measurements?
1.004

4
4087

4
23

2
.082

2
.00006

1
.000060

2
1.000060 
7
1000.

4
4000.00

6
Rounding
1. Only round the final answer.
2. Carry as many significant digits as you
can throughout the problem.
Rounding and Calculators
1. Do all the calculation on the calculator.
2. Arrange the problem to avoid copying an
intermediate answer only to re-enter it
into the calculator.
3. If you must save numbers outside the
calculator, copy several more significant
digits than you think you need.
When to Round Down
• When the digit following the last
significant figure is 4 or less.
Example: 30.24 becomes 30.2
• If the last significant figure is an even
number and the next digit is a 5 with no
other nonzero digits
Example 32.25 becomes 32.2
32.65000 becomes 32.6
When to Round Up
Whenever the digit following the last significant figure is
6 or more.
Example: 22.49 becomes 22.5
If the digit following the last significant figure is a 5
followed by a nonzero digit.
Example: 54.7511 becomes 54.8
If the last significant figure is an odd number and the
next digit is a 5 with no other nonzero digits.
Example 54.75 becomes 54.8
79.3500 becomes 79.4
Scientific Notation
What is Scientific Notation?
• A way of expressing really big
numbers or really small numbers.
• For these types of numbers,
scientific notation is more concise.
Scientific notation consists
of two parts:
• A number between 1 and 10
• A power of 10
Nx
x
10
Standard form to scientific
notation…
• Place the decimal point so that there is one
non-zero digit to the left of the decimal point.
• Count the number of decimal places the
decimal point has “moved” from the original
number. This will be the exponent on the 10.
• If the original number was less than 1, then
the exponent is negative.
If the original
number was greater than 1, then the
exponent is positive.
Examples
• Given: 289,800,000
• Use: 2.898 (moved 8 places)
• Answer: 2.898 x 108
• Given: 0.000567
• Use: 5.67 (moved 4 places)
• Answer: 5.67 x 10-4
Scientific notation to
standard form…
• Move decimal point to the right for
positive exponent 10.
• Move decimal point to the left for
negative exponent 10.
(Use zeros to fill in places.)
Example
• Given: 5.093 x 106
• Answer: 5,093,000 (moved 6
places to the right)
• Given: 1.976 x 10-4
• Answer: 0.0001976 (moved 4
places to the left)
Percent (Experimental) Error
Error
The difference between an exact value
and an estimate or measured value.
Error is always given as a positive value
because it is the size that matters.
Error = Exact value – estimated value
Percentage error = Error X 100%
Exact Value
Example
Exact value of a length is 3.473 m. A measurement gives
3.45 m. What is the percentage error?
% error 
Accepted Value - Experiment al Value
X 100
Accepted Value
3.473  3.45
 100  0.66
3.473
% error = 0.66%
Mass vs. Weight
Mass – The quantity of matter
in an object.
Weight – The gravitational force exerted on
a object by the nearest most
massive body.
Graphing Skills
Graphs tell a story!
Graphing Data
Minimum Graph Requirements
• Title
• Labeled axes
• Legend (if multiple data sets)
Where Does the
Information Come From?

A question is asked.
What kind of ice cream does
everyone like in our class?
How Is the Information
Gathered?

A survey is made.
Chocolate
Vanilla
1111 1
111
Strawberry
1111
Mint & Chip
1111 11
Rocky Road
11
Bubble Gum
1
How Is the Information
Presented?
A bar graph is made.

7
6
5
4
3
2
1
0
Chocolat Vanilla Strawberr Mint & C Rocky R Bubble G
Students
How Is the Information
Presented?
A bar graph is made.

7
6
5
Chocolate
Vanilla
Strawberry
Mint & Chip
Rocky Road
Bubble Gum
4
3
2
1
0
Students
How Is the Information
Presented?

A pie chart is made.
Bubble Gum
Rocky Road
Chocolate
Mint & Chip
Vanilla
Strawberry
How Is the Information
Presented?

A pie chart is made.
Students
Chocolate
Vanilla
Strawberry
Mint & Chip
Rocky Road
Bubble Gum
How Is the Information
Presented?

A line graph is made.
7
6
5
4
3
2
1
0
Chocolate
Vanilla
Strawberr Mint & Ch Rocky Ro Bubble G
Students
How Is the Information
Presented?

A pictograph is made.
Chocolate
Vanilla
Strawberry
Mint & Chip
Rocky Road
Bubble Gum