I. Mathematics

A. Scientific Notation

1. Converting to:

a. Move the decimal point to the left with numbers larger than 1 so that there is only one whole number in front of the decimal.

• The exponent is equal to the number of times you have moved the decimal.

• Since you moved to the left, the exponent is positive!

Examples

67953 = • Now you try!!!

• 117

• 3862

• 10890050260450 =

6.7953 x 104

2.60450 x 105

b. Move the decimal to the right (for numbers less than one) until you have a single whole number in front of the decimal.

• The exponent is equal to the number of times you have moved the decimal.

• Since you moved to the right, the exponent is negative.

Examples

• 0.0036

• = 3.6 x 10 -3

• 0.00000467

• = 4.67 x 10 -6

• Now you try!

• 0.000398

• 0.00257963

2. Converting from:

a. If the exponent is positive, move the decimal to the right the number of times equal to the exponent.

b. If the exponent is negative, move the decimal to the left the number of times equal to the exponent.

• 2.57 x 106

• Converts to:

• 2570000

• 7.995 x 10 -4

• Converts to:

• 0.0007995

Now you try!

• 2.569 x 108

• 7.9356 x 103

• 3.086 x 10 -5

• 9.47 x 10 -2

B. Rounding• Unless you are told otherwise,

in Earth Science, we always round our numbers to the nearest tenth.

• When rounding to the nearest tenth, there should always be one, and only one, number after the decimal point.

• If there is not a value (your answer is a whole number), a zero is placed after the decimal point.

• Remember to round up if the number in the hundredths place is five or greater!

• Examples

• 9.6 g divided by 5 ml = 1.92 g/ml which rounds to

• 1.9 g/ml

• 105.9cm times 2.1 cm times 3.56 cm = 791.7084 cm3 which rounds to

• 791.7 cm3

• Now you try! Round these numbers:

• 786.543

• 125.69

• 95.5897645

C. Calculations

1. Densitya. Actual density is calculated

when mass and volume are known:

b. Mass is determined using either a triple beam or an electronic balance. The unit of mass is grams.

c. Volume is either calculated when length, height and width are known (l x w x h) and the unit is cm3; or volume is determined using a graduated cylinder and the unit is mL.

d. Density is calculated by dividing mass by volume. The units are g/mL

e. Relative density is a comparison between objects or between an object and a liquid.

i. An object is less dense than a liquid if it floats in the liquid.

ii. An object is more dense than a liquid if it sinks in the liquid.

iii. An object has the same density if it is suspended in the middle of the liquid.

f. Density is a characteristic property of a material.

i. This means that density does not change with physical changes to the material (changes in size and/or shape)

ii. Cutting in half creates half the mass and half the volume …density remains the same.

iii. When a material is heated, the molecules move apart…the substance expands.

• This increases the volume.

• Mass remains the same.

• Causing a decrease in density

temperature volume density

• When pressure is applied to a material, the object is forced to take up less space.

• Mass remains the same.

• Volume decreases

• Density increases

pressure volume density

g. Phase changes

• Most substances are

• Least dense in the gas phase

• Most dense in the solid phase

The exception

• When water freezes, the molecules move apart.

• This causes the volume to increase

• Decreasing the density

• WATER IS LESS DENSE AS A SOLID THAN A LIQUID!!!

• WATER IS MOST DENSE AT 4ºC.

2. Percent Deviation

• The formula is given on the front page of your ESRT:

• % deviation =

• difference from accepted value x 100 accepted value

Examples

• A student measuring a desk determines its length to be 6.8 m. The actual length of the desk is 6.2 m. What is the student’s percent deviation?

• Write the formula:

• % dev = dfav x 100 av

• Substitute the information:

• % dev= 0.6m x 100 6.2m

• Calculate the answer:

• % dev = 9.677% which rounds to 9.7%

Now you try!

• Susan estimates Peter’s weight to be 165 lbs. Peter gives his weight as 168 lbs. What is Susan’s percent deviation?

• The volume of a liquid is 45.9 mL. A student measured the volume to be 40.2 mL. What is the percent deviation of the student’s measurement?

3. Proportions/Scale

• Quite often, you are asked to convert a measurement from one scale to another.

• For example, maps are scaled down to accommodate their smaller size. The map scale is provided. Oftentimes it is a simple ratio.

• Whatever the map scale is, that is the ratio you use for converting your measurement.

• For example:

• The map that you are using shows a scale of 1 cm : 500 km.

• That means that every cm measured on the map represents 500 km in real distance.

• If you measured a distance of 5.8 cm on the map, you would use the scale ratio to convert your measurement to km.

• First, you would set up the proportion:

• Cross multiply to solve for x • x km = 5.8 cm x 500 km

1 cm• Your answer is: 2900 km

1cm500km

5.8 cm x km

=

Now you try!

• You know that 1 km = 0.6 miles.

–You measure a distance of 8.9 km.

–Convert it to miles.

• Convert 25 km into cm.–Knowing that 100 cm = 1 m and that 1000 m = 1 km…so you know that 100,000 cm = 1 km!

• Draw a line on your paper.

• The scale for your line is:1 cm : 20 m

• Measure your line and convert that distance to m.

II. Observations

A. An observation is a perception of the environment through the use of our senses.

• It is a statement of fact!

• Using an instrument extends our powers of observation.

B. An inference is an interpretation of an observation.

• An inference is a conclusion based on an observation.

• It can also propose causes for what is observed.

C. An inference about future events is called a prediction.

**Identify the following statements as observations, inferences or predictions:

• 1. The grass is long.

• 2. They never mow their lawn.

• 4. It will be cold this winter.

• 5. The rock is 500 million years old.

• 6. The rock is gray and black.

III. Classification

• Grouping objects together based upon similar characteristics to make information more manageable or easier to understand.

IV. Change

• Change occurs when the properties or characteristics of the environment become different.

• An interface is the boundary between regions of different properties.

• Energy is exchanged across an interface.

• Sometimes change can be balanced…this is referred to as a dynamic equilibrium.

• Change can be determined by calculating the amount of change measured over time

• Rate of change =

• Change in field valueTime

• Or over distance:

• Gradient =

• change in field value Distance

V. The environmentA. Natural resources are

materials and energy found in and/or on the earth.

B. Pollution occurs when the concentration of any substance exists in an amount that harms people, plant or animal life.

VI. Graphing

• In Earth Science we create a number of different types of graphs:

A. The first type (and the most common type) is a line graph.

• The axes of the graph are drawn in the shape of the letter “ L” with the x-axis along the bottom and the y-axis up the left side.

• The data is plotted as a series of points which are connected by a straight or curved line.

• A “best fit” curve goes through a majority of the data points with an equal number of points above and below the line

• On a line graph, the x-axis contains the independent variable and the y-axis contains the dependent variable. Both axes must be labeled with the name of the variable and it’s units.

Time (min)

1. Relationships indicated on linegraphs:

a. When the line drawn looks like an “up escalator”, the relationship between the two variables is said to be a direct relationship.

As the x variable increases, the y variable increases, also.

b. When the line looks like a “down escalator” the relationship is an indirect relationship

As the x variable increases, the y variable decreases.

c. As the x variable increases, the y variable remains the same

d. Sometimes graphs indicate a pattern that is repetitive and, therefore, predictable.

• These relationships are said to be cyclic. As the x variable increases, the y variable increases, decreases, increases etc.

1. Bar graphs

0

10

20

30

40

50

60

70

80

Site 1 Site 2 Site 3 Site 4

Sand

Silt

Clay

B. Other graphs created in EarthScience include:

2. Pie Charts

Hydroelectric

Wind

Solar

Nuclear