Post on 14-Jan-2016
BASICS REVIEW: MATH &
GRAPHING
Units of Measurement
Scientists use the International System of Units, or SI system
This allows easier sharing of data and results
Units of Measurement
SI Base UnitsQUANTITY UNIT ABBREVIATION
Length meter m
Mass gram g
Time second s
Temperature kelvin K
Electric current ampere A
Amount of substance mole mol
Luminous intensity candela cd
Units of Measurement
Derived units (combinations of base units) are used for measurements like area, volume, pressure, weight, force, speed, etc.
The SI system uses prefixes to express very small or very large numbers.
These prefixes are all multiples of 10.
Prefixes Used for Large MeasurementsPREFIX SYMBOL MULTIPLE OF
BASE UNITSCIENTIFIC NOTATION
tetra- T 1 000 000 000 000 1012
giga- G 1 000 000 000 109
mega- M 1 000 000 106
kilo- k 1000 103
hecta- h 100 102
deka- dk 10 101
Prefixes Used for Small Measurements
PREFIX SYMBOL MULTIPLE OF BASE UNIT
SCIENTFIC NOTATION
deci- d 0.1 10-1
centi- c 0.01 10-2
milli- m 0.001 10-3
micro- µ 0.000 001 10-6
nano- n 0.000 000 001 10-9
pico- p 0.000 000 000 001 10-12
Units of Measurement
If you are converting to a smaller unit, multiply the measurement to get a bigger number.
Example:Write 1.85 m as centimeters.
Units of Measurement
If you are converting to a larger unit, divide the measurement to get a smaller number.
Example:Write 185 cm as meters.
Units of Measurement: Practice
1. Write 550 millimeters as meters.
2. Write 3.5 seconds as milliseconds.
3. Convert 1.6 kilograms to grams.
4. Convert 2500 milligrams to kilograms.
5. Convert 4 centimeters to micrometers.
6. Change 2800 millimoles to moles.
7. Change 6.1 amperes to milliamperes.
8. Write 3 micrograms as nanograms.
Units of Measurement
Most often, you will measure things like time, length, mass, and volume.
Length = a measure of the straight-line distance between two points
Mass = a measure of the amount of matter in an object
Volume = a measure of the size of a body or region in three-dimensional space
Units of Measurement
Weight and mass are not the same thing.
Weight = a measure of the gravitational force exerted on an object
Writing Numbers in Scientific Notation Scientists sometimes need to express
measurements using numbers that are very large or very small.
To reduce the number of zeros, values can be expressed as a simple number multiplied by a power of 10.
This is called scientific notation.
Writing Numbers in Scientific Notation
Power of 10 Decimal Equivalent
104 10 000
103 1000
102 100
101 10
100 1
10-1 0.1
10-2 0.01
10-3 0.001
Writing Numbers in Scientific Notation: Practice
Write the following measurements in scientific notation:1. 800 000 000 m
2. 0.0015 kg
3. 60 200 L
4. 0.000 95 m
5. 8 002 000 km
6. 0.000 000 000 06 kg
Writing Numbers in Scientific Notation: Practice
Write the following measurements in long form:1. 4.5 x 103 g
2. 6.05 x 10-3 m
3. 3.115 x 106 km
4. 1.99 x 10-8 cm
Using Scientific Notation
When using scientific notation in calculations, you follow the math rules for powers of 10.
When you multiply two values, add the powers of 10.
When you divide two values, subtract the powers of 10.
Using Scientific Notation
Perform the following calculations:1. (5.5 x 104 cm) x (1.4 x 104 cm)
2. (2.77 x 10-5 m) x (3.29 x 10-4 m)
3. (4.34 g/mL) x (8.22 x 106 mL)
4. (3.8 x 10-2 cm) x (4.4 x 10-2 cm) x (7.5 x 10-2 cm)
5. (3.0 x 104 L) / 62 s
6. (6.05 x 107 g) / (8.8 x 106 cm3)
7. (5.2 x 108 cm3) / (9.5 x 102 cm)
8. (3.8 x 10-5 kg) / (4.6 x 10-5 kg/cm3)
Using Significant Figures
Precision = the exactness of a measurement
To show the precision of a measured quantity, scientists use significant figures.
Significant figure = a prescribed decimal place that determines the amount of rounding off to be done based on the precision of the measurement
Using Significant Figures Accuracy = a description of how close a
measurement is to the true value of the quantity measured
A measured quantity is only as accurate as the tool used to make the measurement.
When you use the measurements in calculations, the answer is only as precise as the least precise measurement used in the calculation – the measurement with the fewest significant figures.
Using Significant Figures: Practice Perform the following calculations, and
write the answer with correct number of significant figures.1. 12.65 m x 42.1 m
2. 3.02 cm x 6.3 cm x 8.225 cm
3. 3.7 g / 1.083 cm3
4. 3.244 m / 1.4 s
Rules for Determining the Number of Significant Figures
1) All nonzero digits are significant.Example: 1246
2) Any zeros between significant digits are also significant.Example: 1206
3) If the value does not contain a decimal point, any zeros to the right a nonzero digit are not significant.
Example: 1200
Rules for Determining the Number of Significant Figures
4) Any zeros to the right of a significant digit and to the left of a decimal place are significant.Example: 1200.
5) If a value has no significant digits to the left of a decimal point, any zeros to the right of the point, and to the left of a significant digit, are not significant.Example: 0.0012
Rules for Determining the Number of Significant Figures
6) If a measurement is reported that ends with zeros to the right of a decimal point, those zeros are significant.Example: 0.1200
GRAPHING SKILLS
Presenting Scientific Data Line graphs are best for displaying data
that can change. The x-axis usually shows the
independent variable. The y-axis usually shows the
dependent variable.
Presenting Scientific Data Bar graphs are best for comparing
similar data for several individual items or events.
These graphs often clearly show how large or small the differences in individual values are.
Pie charts are best for displaying data that are parts of a whole.
Line Graphs
Line graphs show the relationship between an independent and a dependent variable very clearly.
The independent variable is plotted on the x-axis.
The dependent variable is plotted on the y-axis.
You have to be sure to properly label both axes and include the units for the values.
Line Graphs
Scatter Plots A scatter plot is very similar to a line graph. The data points are plotted on the graph using the x-
and y-axes. They are often used to find trends in data by using a
best-fit line. This line represents all of the data points without
necessarily going through all of them. To find a best-fit line, pick a line that is equidistant
from as many data points as possible. This line can show a trend more clearly and points
on the line can be used to determine its slope.
Scatter PlotsJacket Sales
Temperature (°C) Number of Jackets Sold
110 0
100 1
90 3
80 5
70 25
60 49
50 87
40 104
30 276
Bar Graphs
Bar graphs are used to compare data quickly and to identify trends.
The data represented by these graphs are represented accurately, but it isn’t easy to draw conclusions quickly.
Bar Graphs
Pie Charts
Pie charts provide an easy way to visualize how parts make up a whole.
They are typically made from percentage data.
To make a pie chart, we can estimate the portions of the circle that each percentage would require.
We can also use protractors, which is helpful when the data can’t be converted into simple fractions.
Pie Charts
Student Grades
Letter Grade Number of Students
A 4
B 12
C 10
D 2