real numbers (as opposed to fake numbers?) real numbers real numbers are every number. therefore,...
TRANSCRIPT
Real Numbers
• Real Numbers are every number.
• Therefore, any number that you can find on the number line.
• Real Numbers have two categories.
What does it Mean?
• The number line goes on forever.• Every point on the line is a REAL
number.• There are no gaps on the number line.• Between the whole numbers and the
fractions there are numbers that are decimals but they don’t terminate and are not recurring decimals. They go on forever.
Irrational Numbers
•An irrational number is a number that cannot be written as a fraction of two integers.
•Irrational numbers written as decimals are non-terminating and non-repeating.
Rational Numbers
•A rational number is a real number that can be written as a fraction.
•A rational number written in decimal form is terminating or repeating.
Try this!
• a) Irrational
• b) Irrational
• c) Rational
• d) Rational
• e) Irrational66 e)
d)
25 c)
12 b)
2 a)
115
What are integers?
• Integers are the whole numbers and their opposites.
• Examples of integers are 6-120186-934
Types of Integers
• Natural Numbers(N): Natural Numbers are counting numbers from 1,2,3,4,5,................N = {1,2,3,4,5,................}
• Whole Numbers (W): Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5,...............W = {0,1,2,3,4,5,..............} W = 0 + N
Comparing Rational and Irrational Numbers
• When comparing different forms of rational and irrational numbers, convert the numbers to the same form.
Compare -3 and -3.571 (convert -3 to -3.428571…
-3.428571… > -3.571
37
37
Ordering Rational and Irrational Numbers
• To order rational and irrational numbers, convert all of the numbers to the same form.
• You can also find the approximate locations of rational and irrational numbers on a number line.
Example• Order these numbers from least to
greatest. ¹/₄, 75%, .04, 10%, ⁹/₇
¹/₄ becomes 0.2575% becomes 0.750.04 stays 0.0410% becomes 0.10
⁹/₇ becomes 1.2857142…
Answer: 0.04, 10%, ¹/₄, 75%, ⁹/₇