Units of Measurement Scientists use the International System of Units, or SI system This allows easier sharing of data and results.

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