2. Real Numbers and Number Lines

3. Whole Numbers whole numbers natural numbers This figure shows a set of whole numbers. The whole numbers include 0 and the natural, or counting, numbers. The arrow to the right indicates that the whole numbers continue indefinitely. Zero is the least whole number. 123456789101112130

4. Integers integers A number line can be used to represent a set of integers. Integers include 0, the positive integers, and the negative integers. The arrows indicate that the numbers go on forever in both directions. 1234560-2-3-4-5-6 negative integerspositive integers

5. Rational Numbers rational numbers A number line can also show rational 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

6. terminatingnonterminating Decimals may be terminating or nonterminating. 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.

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

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

9. Real Numbers Real numbers Real numbers include both rational and irrational numbers.

10. coordinate origin The number that corresponds to a point on a number line is called the coordinate of the point. Coordinate 0 is called the origin. 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

11. 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

12. absolute value One way to calculate the measurement of a distance is by using absolute 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.

13. Real Numbers Irrational Numbers Integers Rational Numbers Whole Numbers Natural Numbers -5/2 2/3 0.65 0.9 -5-7 0 3 1 2 0.12122... 0.010011...

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

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