Real Numbers and Number Lines

Whole Numbers

This figure shows a set of whole numberswhole numbers. The whole numbers include 0 and the naturalnatural, or counting, numbersnumbers. The arrow to the right indicates that the whole numbers continue indefinitely. Zero is the least whole number.

1 2 3 4 5 6 7 8 9 10 11 12 130

Integers

A number line can be used to represent a set of integersintegers. Integers include 0, the positive integers, and the negative integers. The arrows indicate that the numbers go on forever in both directions.

1 2 3 4 5 60-1-2-3-4-5-6negative integers positive integers

Rational Numbers

A number line can also show rational numbersrational numbers. A rational number is any number that can be written as a fraction, a/b, where a and b are integers and b cannot equal 0. There are infinitely many rational numbers between two integers. Rational numbers can also be represented by decimals.

3/8 = 0.375 2/3 = 0.666... 0/5 = 0

Decimals may be terminatingterminating or nonterminatingnonterminating.0.375 and 0.49 are terminating decimals.0.666... and -0.12345... are nonterminating decimals.

Some nonterminating decimals have a repeating pattern.0.171717... repeats the digits 1 and 7 to the right of the decimal point.

Each rational number can be expressed as a terminating decimal or a nonterminating decimal with a repeating pattern.

When a number(s) has a line over the top of it, like 0.17, it is read as zero point one seven repeating.

Irrational Numbers

Decimals that are nonterminating and do not repeat are called irrational numbersirrational numbers.6.028716 ... and 0.101001000... appear to be irrational numbers

Real Numbers

Real numbersReal numbers include both rational and irrational numbers.

The number that corresponds to a point on a number line is called the coordinatecoordinate of the point. Coordinate 0 is called the originorigin.

For any two points on a line and a given unit of measure, there is a unique positive real number called the measure of the distance between the points.

measure

AB

Points on a line are paired with the real numbers, and the measure of the distance between two points is the positive difference of the corresponding numbers

AB

measure = a - b

One way to calculate the measurement of a distance is by using absolute valueabsolute value. The absolute value of a number is the number of units a number is from zero on the number line. In symbols, the absolute value is denoted by two vertical slashes.

Real Numbers

Irrational Numbers

Integers

Rational Numbers

Whole Numbers

Natural Numbers

-5/2

2/3

0.65

0.9

-5-7

0

31

2

0.12122...

0.010011...

All information taken from the Glencoe Geometry – Concepts and Applications, pg. 50-54.

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