IB Maths Studies/Number and Algebra

From Wikibooks, open books for an open world
Jump to: navigation, search

The Number Sets of N, Z, Q and R

N - Natural Numbers. These are in the set (1, 2, 3...)

We say "March has 31 days" or "There are 15 students in my math class" We count with the numbers 1, 2, 3, 4...
We also use these numbers for ordering. We say "This is the first year of my math studies course" or "Alison came second in the race"

Z - Integers. The set includes (...-3, -2, -1, 0, 1, 2, 3...)

Q - Rational Numbers. These are the fractions created by dividing one integer by another. This set can include decimals numbers as long as they can be transformed into a fraction.

R - The Real Numbers. This includes all of the above. In addition, it includes the irrational numbers such as pi (3.14...) or e (2.71...). Irrationals are real decimal numbers that follow no pattern and are without end. Any decimal that ends or follows a pattern is a rational number.

Real Numbers can be understood best by comparing them with their evil twin - the imaginary numbers. Imaginary numbers are found when someone tries to take the square root of a negative number. Since, logically speaking, this is a no no, mathematicians use "i" to represent an imaginary number. Luckily, we do not use imaginary numbers in Math Studies. The rule of thumb for Real numbers is "if you can count it, it is real."

Significant Figures

Unless otherwise written, answers in IB Math Studies are always to be given to three significant figures. So, what, you are dying to know, is a significant figure? Significant figures are like gremlins, they have to follow certain rules or things get out of control. So here are the rules for keeping Gizmo safe:

1. Always count nonzero digits

Example: 348 has three significant figures. 27 has two.

2. Never count leading zeros

Example: 021 and 0.021 both have two significant figures

3. Always count zeros which fall somewhere between two nonzero digits

Example: 20.8 has three significant figures, while 0.00104009 has six

4. Zeros after the last non-zero digit are not significant

Example: 498,000 has three significant figures