Download Real Number System Dichotomous Key

Real Number System Dichotomous Key
Directions: Use the dichotomous key below to determine what kind of number you
have.
1. Does the number have a fraction or decimal?
a. Yes. Go to 2.
b. No. Go to 6.
2. Which does the number have?
a. Fraction. Simplify it by dividing. Go to 3.
b. Decimal. Go to 4.
3. Does the divided fraction have a decimal?
a. Yes. Go to 4.
b. No. go to 6.
4. Does the decimal terminate?
a. Yes. The number is rational (also real).
b. No. Go to 5.
5. Does the decimal repeat?
a. Yes. The number is rational (also real).
b. No. The number is irrational (also real).
6. Is the number negative?
a. Yes. It is an integer (also rational, real).
b. No. Go to 7.
7. Is the number 0 (zero)?
a. Yes. It is a whole number (also integer, rational, real).
b. No. It is a natural/counting number (also whole, integer, rational,
real).
Also important:
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Real numbers includes natural/counting numbers, whole numbers, integers,
rational and irrational numbers.
Natural/counting numbers are the set of counting numbers {1, 2, 3, 4, ...}.
Whole numbers include the set of all the natural/counting numbers and zero
{0, 1, 2, 3…}.
Integers include the set of whole numbers and their opposites {…-2, -1, 0, 1,
2…}.
Rational numbers include all numbers that can be expressed as fractions in
the form where a and b are integers and b does not equal zero (e.g.,
, ,2.3, 75%, 4.595959…) .
Irrational numbers include all non-repeating, non-terminating decimals. An
irrational number cannot be written in fraction form {e.g., ,
,
1.232332333…}.
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All natural/counting numbers are also whole numbers, integers, rational
numbers, and real numbers.
All whole numbers are also integers, rational numbers, and real numbers.
All integers are also rational numbers and real numbers.
All rational numbers are real numbers.
All irrational numbers are real numbers.
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Some
Some
Some
Some
Some
whole numbers are also natural/counting numbers.
integers are also whole numbers.
rational numbers are also integers.
real numbers are rational numbers.
real numbers are irrational numbers.