real numbers

REAL NUMBERS

(as opposed to fake numbers?)

Two Kinds of Real Numbers

•Rational Numbers

•Irrational Numbers

Branching Real Numbers

Real Numbers

Rational Irrational

Now let’s break these subsets down

further!

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).

Examples of Rational Numbers

•16•1/2•3.56

•-8•1.3333…•- 3/4Can you write 16 as a ratio?

Now try writing -8 as a ratio!

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).

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?

Integers

One of the subsets of rational numbers

So what do integers branch off of?

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)

What are integers?

• Integers are the whole numbers and their opposites.

• Examples of integers are 6-120186-934

What do you notice about these integers?

Whole Numbers

One of the subsets of rational numbers and

integers

So what do whole numbers branch off of?

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 …

Natural Numbers

One of the subsets of rational numbers, integers and whole

numbers

So what do natural numbers branch off of?

Natural Numbers

• All of your counting numbers

• What numbers do you count with?

Classify the following Numbers

• What subset(s) do the following numbers belong to? Remember they could belong to more than one!

• 0• Whole, Integers, Rational, and Real

Classify the following Numbers (Con’t)

• 4• Natural, Whole, Integer, Rational, Real

• -9• Integer, Rational, Real

• Π • Irrational, Real

Classify the following Numbers (Con’t)

• 3/4 or 0.75• Rational and Real

• 4• Natural, Whole, Integer, Rational, Real

• 15 • Irrational, Real