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.

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.

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:

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:

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.

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.

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)