 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.
 Support easyphysics.net by visiting our advertisers' websites. 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. 3600 seconds = 60 minutes = 1 hour 100 centimeters = 1 meter 1000 grams = 1 kilogram Section 2: Scientific NotationWhen 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. 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 3: Significant Digits

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

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 4: GraphThree 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. Another relationship is the quadratic relationship. The equation is y = kx2, where k is a constant. The third equation is an inverse relationship, expressed by xy = k, where k is a constant.  Section 5: Trigonometry

Trigonometry is also important in physics. When you have a right-angled triangle, the following relationships are true:     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 6: Chapter 1 QuizTake the Chapter 1 Quiz to see how well you can do!

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