Section 2.6: Rational and Irrational Numbers
- Definition of a Rational Number
A rational number is a number that can be written as the ratio of two integers. Rational numbers can be written as repeating or terminating decimals. - Relationships among sets of numbers
Standard Forms of a Fraction
If p and q are positive integers, then p/q and -p/q are called the standard forms of a fraction. A reduced fraction is a fraction in standard form such that there is no integer (other than 1 or- 1) that divides into both p and q. - Pythagorean
Theorem
- Definition of Square Root
The square root of a a nonnegative number x, written
x,
is that nonnegative number such that xx=x
The perfect squares you should know for this book are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, and 196.
- Definition of an Irrational Number
An irrational number is a number whose decimal representation does not terminate or repeat. - Definition of a Real Number
The set of real numbers is the set of numbers consisting of all numbers that are either rational or irrational. Any real number is- Positive, negative, or zero
- A rational number or an irrational number
- Expressible as a terminating, a repeating, or a nonterminating and
nonrepeating decimal
a. If it terminates, it is rational.
b. If it eventually repeats, it is rational.
c. If it does not terminate or eventually repeat, it is irrational.