Basic Skills
 

Welcome to the first chapter of easyphysics.net!

If you are new to studying physics, you will need to be familiar with some basic algebra. In this chapter, we will review important math techniques. Don't let numbers and calculations intimidate you. This chapter will help you become more familiar with math.

 

1. Units
2. Scientific Notation
3. Significant Digits
4. Graph
5. Trigonometry
6. Chapter 1 Quiz

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  Section Section 1: Units

The metric system of measurement is the standard in the world. The fundamental units include the second (s) for time, the meter (m) for length, and the kilogram (kg) for mass.

You should know how to convert from one unit to another.

 

Check!

3600 seconds = 60 minutes = 1 hour
100 centimeters = 1 meter    
1000 grams = 1 kilogram    

 

  Section Section 2: Scientific Notation

When expressing an extreme large number such as the mass of Earth, or a very small number such as the mass of an electron, scientists use the scientific notation. The basic format of scientific notation is M * 10n, where M is any real numbers between 1 and 10 and n is a whole number.

 

Check!

100 = 1
101 = 10
102 = 10 * 10 = 100
103 = 10 * 10 * 10 = 1000
10-1 = 1 / 10 = 0.1
10-2 = 1 / 10 / 10 = 0.01
10-3 = 1 / 10 / 10 / 10 = 0.001

For example, the mass of Earth is about

6,000,000,000,000,000,000,000,000 kg

and can be written as 6.0 * 1024 kg.

Also, the mass of an electron is

0.000000000000000000000000000000911 kg

and can be expressed as 9.11 * 10-31 kg.

QUESTION: Express 8.213 * 102 in decimal number.

QUESTION: Solve 4 * 102 + 3.2 * 103.

 

  Section Section 3: Significant Digits

The significant digits represent the valid digits of a number. The following rules summarize the significant digits:

 

Check!

  1. Nonzero digits are always significant.
  2. All final zeros after the decimal points are significant.
  3. Zeros between two other significant digits are always significant.
  4. Zeros used solely for spacing the decimal point are not significant.

The table below is an example:

values # of significant digits
5.6 2
0.012 2
0.0012003 5
0.0120 3
0.0012 2
5.60 3

In addition and subtraction, round up your answer to the least precise measurement. For example:

24.686 + 2.343 + 3.21 = 30.239 = 30.24

because 3.21 is the least precise measurement.

In multiplication and division, round it up to the least number of significant digits. For example:

3.22 * 2.1 = 6.762 = 6.8

because 2.1 contains 2 significant digits.

In a problem with the mixture of addition, subtraction, multiplication or division, round up your answer at the end, not in the middle of your calculation. For example:

3.6 * 0.3 + 2.1 = 1.08 + 2.1 = 3.18 = 3.2.

QUESTION: Solve 5.123 + 2 + 0.00345 - 3.14.

QUESTION: Solve -9.300 + 2.4 * 3.21.

 

  Section



Check!
Section 4: Graph

Three types of mathematical relationships are most common in physics.

One of them is a linear relationship, which can be expressed by the equation y = mx + b where m is the slope and b is the y-intercept.

A graph representing the Linear Relationship

Another relationship is the quadratic relationship. The equation is y = kx2, where k is a constant.

A graph representing the Quadratic Relationship

The third equation is an inverse relationship, expressed by xy = k, where k is a constant.

A graph representing the Inverse Relationship

 

  Section Section 5: Trigonometry

Trigonometry is also important in physics. When you have a right-angled triangle, the following relationships are true:

  Check!
Formula for sine A right triangle to explain Sine, Cosine, and Tangent
Formula for Cosine
Formula for Tangent

Trigonometry will become important when you study vectors.

QUESTION: You are looking up at the top of a tree that is 10 m apart from you. If the tree is 15 m taller than you, at what angle are you looking upward? (e.g. 30.0)

 

  Section Section 6: Chapter 1 Quiz

Take the Chapter 1 Quiz to see how well you can do!


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