1.7 Notes
_Real_ Numbers _System_
Name all sets to which
Rational Numbers
Irrational Numbers
each number belongs:
30 N, W, Z, Q, R
0.75
-1
√
Whole numbers
Integers
–11 Z, Q, R
Natural
5
Q, R
Numbers
√
I, R
0 N, W, Z, Q, R
√ = –3 Z, Q, R
Real Numbers
Natural
( counting )numbers: begin with the number _1___ .
Whole numbers build from the set of natural numbers by adding the number __0__ .
Integers build from the set of _whole_ by adding _negative_ “whole” numbers.
Can be both positive and negative, but there are no decimals !
Rational Numbers are RATIOs of two integers (fractions)
The set builds from Integers by adding fractions.
Also consist of terminating and repeating _ decimals.
Irrational does not build up from the previous sets. It consists of not rational numbers
with non-terminating , non-repeating decimals.
1. Simplify
2. Choose the STARTING POINT
If my number…
has
NO decimal part,
NO negative sign
It is NOT zero
Examples:
3. Move toward REAL Numbers
(ANALYZE parts of the number)
has
has
NO decimal part, NO decimal part,
NO negative sign,
Is NEGATIVE
is ZERO (0)
Examples:
Example:
has
DECIMAL PART
has
DECIMAL
Ratio,
Terminating Decimal
Repeating Decimal
PART
Examples:
Nonterminating,
Non- Repeating
Then start from…
Natural
Whole
Integers
Rational STOP!
Choose the correct term to complete the sentence:
Numbers with decimals that are not repeating or terminating (are, are not) irrational numbers.
Irrational