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(as opposed to fake numbers?)
REAL NUMBERS (as opposed to fake numbers?)
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Two Kinds of Real Numbers
Rational Numbers Irrational Numbers
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Branching Real Numbers
Rational Irrational Now let’s break these subsets down further!
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Rational Numbers A rational number…
is a real number that can be written as a ratio (fraction) of two integers. written in decimal form is terminating (ends) or repeating (same pattern of numbers).
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Examples of Rational Numbers
16 1/2 3.56 -8 1.3333… - 3/4 Can you write 16 as a ratio? Now try writing -8 as a ratio!
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Irrational Numbers An irrational number
is a number that cannot be written as a ratio (fraction) of two integers. written as decimals are non-terminating (never end!) and non-repeating (no pattern).
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Examples of Irrational Numbers
Square roots of non-perfect “squares” Pi 17 What is the square root of 17? What is another non-perfect square?
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Integers One of the subsets of rational numbers
So what do integers branch off of?
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Integers Integers are rational numbers because they can be written as fraction with 1 as the denominator. *Remember* Rational numbers can be written as a ratio (or in other words, a fraction)
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What are integers? Integers are the whole numbers and their opposites.
Examples of integers are 6 -12 186 -934 What do you notice about these integers?
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Whole Numbers One of the subsets of rational numbers and integers
So what do whole numbers branch off of?
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Whole Numbers All positive numbers that are counting numbers plus zero. How can you remember that zero goes with whole numbers? Examples: 0, 1, 2, 3, 4, 5 …
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Natural Numbers One of the subsets of rational numbers, integers and whole numbers So what do natural numbers branch off of?
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Natural Numbers All of your counting numbers
What numbers do you count with?
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Classify the following Numbers
What subset(s) do the following numbers belong to? Remember they could belong to more than one! Whole, Integers, Rational, and Real
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Classify the following Numbers (Con’t)
4 Natural, Whole, Integer, Rational, Real -9 Integer, Rational, Real Π Irrational, Real
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Classify the following Numbers (Con’t)
3/4 or 0.75 Rational and Real 4 Natural, Whole, Integer, Rational, Real 15 Irrational, Real
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