____________________Examples:

All the numbers that can be written as fractions. Each fraction must have a nonzero denominator.

Rational numbers can be a terminating decimal. For example:

Rational numbers can also be a repeating decimal. For Example:

___________________ Examples:

Numbers that cannot be written as fractions.

Their decimal representations neither terminate nor repeat, they go on infinitely.

If a positive rational number is not a perfect square, then its square root is irrational.

____________________Examples:

_________________Examples:

__________________Examples:

2.1 Using Integers and Rational Numbers

REAL NUMBERS

The Number Line

Integers = {…, -2, -1, 0, 1, 2, …}Whole Numbers = {0, 1, 2, …}Natural Numbers = {1, 2, 3, …}

To Graph a set of numbers means to locate and mark the points on the number line.

Graph {-1, 0, 2}

We can also use the number line to compare numbers. If you had to tell someone how to use the number line to determine which number it bigger,

what would you tell them??

___________________________________________________

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In Astronomy, a star’s color index is a measure of the temperature of the star.

The greater the color index, the cooler the star. Order the stars in the table from hottest to coolest.

Stars Rigel Arneb Denebola

Shaula

Color Index -0.03 .21 .09 -.22

Opposites: Two numbers that are the same distance from 0 on a number line but are on opposite sides of 0. - Use the number line below to graph a set of opposites

Describe how to find a set of opposites _______________________________________________

____________________________________________________________________________________

Absolute Value asks a question about a given number. The number is surrounded by vertical bars and the question is,

“On the number line, how far is this number from 0?”

Examples:

A Conditional Statement has a hypothesis and a conclusion.

One type of conditional statement is called and “If-then” statement. The “if” contains the conditions called the hypothesis, and the “then” states what will happen under those conditions also called the conclusion.

“If-then” statements are either true or false. The statement if true only if the conclusion is always true.

Example #1 : If a football team scores two points, then they must have gotten a safety.

Example #2 : If a number is a rational number, then the number is positive.

To prove that an “If-then” statement is false we use a counterexample, an example that proves the “then” part inaccurate or not entirely true all of the time.

Look back at the two examples and give counterexamples for each.

Example #1: ______________________________

Example #2: ______________________________

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