REAL NUMBERS Elis Meisolichati as opposed to fake
REAL NUMBERS Elis Meisolichati (as opposed to fake numbers? )
Objective • Identify the parts of the Real Number System • Define rational and irrational numbers • Classify numbers as rational or irrational
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.
Two Kinds of Real Numbers • Rational Numbers • Irrational Numbers
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.
Examples of Rational Numbers • 16 • 1/2 • 3. 56 • -8 • 1. 3333… • - 3/4
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.
Irrational numbers can be written only as decimals that do not terminate or repeat. They cannot be written as the quotient of two integers. If a whole number is not a perfect square, then its square root is an irrational number. Caution! A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits.
Try this! • a) Irrational • b) Irrational • c) Rational • d) Rational • e) Irrational
Comparing Rational and Irrational Numbers • When comparing different forms of rational and irrational numbers, convert the numbers to the same form. Compare -3 37 and -3. 571 (convert -3 37 to -3. 428571… > -3. 571
Practice •
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.
-1 + 3 = ? a) -4 b) -2 c) 2 d) 4 Answer Now
-6 + (-3) = ? a) -9 b) -3 c) 3 d) 9 Answer Now
Which is equivalent to -12 – (-3)? a) 12 + 3 b) -12 + 3 c) -12 - 3 d) 12 - 3 Answer Now
7 – (-2) = ? a) -9 b) -5 c) 5 d) 9 Answer Now
Conclution 1) If the problem is addition, follow your addition rule. 2) If the problem is subtraction, change subtraction to adding the opposite (keep-change) and then follow the addition rule.
State the rule for multiplying and dividing integers…. If the signs are the same, the answer will be positive. If the signs are different, the answer will be negative.
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