Unit 1-Math and Methods

Lesson 1 – SI Units and Dimensional Analysis

SI Units (Le Systéme Internationale)

A ______is a defined unit in a system of measurement

There are ______standard units in SI.

Quantity / Standard Unit

Derived units of measurement

A derived unit is any unit ______

In other words:

The main derived units used in this class are and .

Volume

Volume =

Volume can be found mathematically

(Vrect. prism= )

Volume can also be measured ______

By definition 1 cm3 = ______

Density

Density =

D=

Units for mass are usually ______

Units for volume can either be ______

Remember :

Many known densities are listed in your reference packet, these will be useful throughout the semester.

Prefixes

Prefix / Symbol / Factor / Scientific Notation
giga / 1 000 000 000 / 109
mega / 1 000 000 / 106
1000 / 103
100 / 102
10 / 101
BASE UNIT / 1 / 100
1/10 / 10-1
1/100 / 10-2
1/1 000 / 10-3
micro / 1/1 000 000 / 10-6
nano / 1/1 000 000 000 / 10-9
pico / 1/1 000 000 000 000 / 10-12

Why do we use the metric system?

Advantages

Unit Equalities – Some Examples

1 meter = 1 mole =

1 L = 1 shirt =

1 km = 1 kg =

All unit equalities can be turned into conversion factors if needed.

Dimensional Analysis

Process for ______

The ______(1 km = 1000 m) becomes the______:

Using Dimensional Analysis

Multiply the starting unit by ______

Example: Convert 4.6 m to km

4.6 m x ______= km

Examples

Convert between the following measurements using dimensional analysis (show your conversion factors):

1.) 2.34 mg x ______= g

2.) .98 mol x ______= atoms

3.) 1,098 mL x ______= L

4.) 5 km x ______x______= cm

Multiple Unit Dimensional Analysis

Convert 455 km/hr to m/s

Convert 6.67g/mL to mg/L

Convert 45m/s to mm/hr

(Honors) Converting Cubed Units

Express 4563 mm3 in m3

Express 35.6 mol/m3 in atoms/cm3

Lesson 2 – Sci. Notation, Accuracy, and Significant Figures

Accuracy Versus Precision

What is the difference between accuracy and precision?

Precision:

Accuracy:

Calculating Accuracy (Percent Error)

Percent error allows you to ______your answer to ______

______to see how accurate you were.

The “actual answer” is referred as the ______.

“Your answer” is referred to as the ______.

% Error =

Example

The density of water is known to be 1.00 g/mL. You measure the mass and volume of a water sample and calculate its density to be 1.18 g/mL. What is your percent error?

Scale Reading and Uncertainty

Uncertainty:

Uncertainty exists in not in .

Counted quantities are ______.

Uncertainty in Measurements

The ______spot is uncertain.

Measurements between users

What is the length of this arrow?

Likely we have many different possible answers based on our own eyes.

Significant Figures

Significant Figures:

Digits with meaning:

How to determine which figures are significant in a given number

All non-zero digits (1-9)______.

The zeros in a number are ______significant, depending on their position in the number

*There are a standard set of rules for figuring out whether or not zeros are significant.

Rules for zeros:

These are the ones that disappear when you write the number in scientific notation.

E.g. 1005 kg (4 sig. fig) and 1.03 (3 sig. fig)

E.g. 0.02 (1 sig. fig) and 0.0026 (2 sig. fig)

0.0200g (3 sig. fig), 3.0 cm (2 sig. fig), 5000 (1 sig. fig)

Practice

How many significant figures are in:

400.0 ______

4000 ______

4004 ______

0.004

______

Scientific notation

Scientific notation has two purposes:

1.

Scientific notation has three parts: a ______that is 1 or greater and less than 10, a ______and a ______:

Scientific Notation Practice

Convert to scientific notation:

1) 89540 = ______

2)0.000345 = ______

3)0.0041 = ______

4)7890000 = ______

5)23000 = ______

Convert to standard form:

1)6.72 x 10³ = ______

2)2.341 x 10ˉ³ = ______

3)5.6 x 10² = ______

4)1.29 x 10° = ______

5)4.78 x 10ˉ² = ______

Significant Figures

Pacific to Atlantic Rule

Pacific = ______

Start from the Pacific (left hand side), ______with

the first 1-9 integer ______.

Examples

20.0 = ______

0.00320400 = _____

1000. = ______

Atlantic Rule to Pacific

Atlantic = ______

Start from the Atlantic (right hand side), every digit beginning with the first 1-9 integer is significant

Examples

100020 = ______sig digits

1000 = ______sig digits

Review Questions

Determine the number of significant figures in the following:

1.1005000 cm

2.1.005 g

3.0.000125 m

4.1000. km

5.0.02002 s

6.2002 mL

7.200.200 days

More Practice

Determine the number of significant figures in:

1.72.3 g

2.60.5 cm

3.6.20 m

4.0.0253 kg

5.4320 years

6.0.00040230 s

7.4.05 moles

8.4500. L

Significant Figures when in Scientific Notation

The number of significant figures in a measurement that is in scientific notation is simply the

______of the measurement.

1) 4.5 x 10³ has ______significant figures

2)5.234 x 10² has ______significant figures

3)9.65 x 10ˉ³ has ______significant figures

What about when you add two measurements?

When you ______, your answer

must have the same number of digits ______as

the value with the ______digits to the right of the decimal point.

Ex 456.865g + 2g = 458.865g (do the calculation first)

Since 2g has no ______, neither can your

answer, which would be ______(three sig figs)

Practice

Add the following measurements: (don’t forget conversions)

2.6g + 3.47g + 7.678g =

30.0 mL – 2.35 mL =

5.678 cm + 3.76 cm =

What about when you multiply/divide two measurements?

When you ______, your answer

must have the same number of significant figures as ______

______.

*This does not apply to ______or

______, they will not impact the number of significant figures.

Ex. Find the density of an object with a mass of 2.6g and a volume of 300 mL (Density = mass/volume)

Practice

24m x 13.6m x 3.24m =

47g ÷ 32.34 mL =

40m ÷ 4.3 sec =

Lesson 3 – Literal Equations

A ______is an equation that uses variables to represent known values.

Using algebra skills, literal equations can be ______to solve for any of the values that are in the equation.

Examples:

Solve D = m/v for the volume

Solve D = m/v for the mass

Solve PV = nRT for the temperature

Solve PV = nRT for the pressure

Applying the Skill (Densities are in the Reference Packet)

What is the mass of a piece of copper that has a volume of 8.9 cm3 ?

What is the volume of a sample of sulfur dioxide that has a mass of 26.2 g ?

Unit 1-Math and Methods