NUMBER SYSTEMS
Quick Revision
Review the key ideas, definitions and rules from the chapter.
Natural Numbers
Natural Numbers are the numbers commonly used for counting.
There is no largest Natural Number.
Zero
Zero represents the absence of something.
Whole Numbers
Whole Numbers include zero together with the Natural Numbers.
Integers
Whole Numbers are not enough when subtraction gives a negative result.
Rational Numbers
A Rational Number can be written in the form:
where p and q are integers and:
Irrational Numbers
Irrational Numbers cannot be written in the form p/q, where p and q are integers and q ≠ 0.
Their decimal expansions are non-terminating and non-recurring.
Real Numbers
Real Numbers include both Rational and Irrational Numbers.
Decimal Representation
A Rational Number can have a decimal expansion that is either terminating or recurring.
When Does a Rational Decimal Terminate?
First write the Rational Number in its simplest form.
Why are 2 and 5 special?
Our decimal system is based on powers of 10.
So denominators containing only 2s and 5s can be converted into a power of 10.
Recurring Decimal → Fraction
Use a variable for the recurring decimal, multiply by a suitable power of 10, then subtract.
The Big Picture
Each new number system extends what we can represent.
Irrational Numbers are also part of the Real Numbers.
READY TO TEST YOURSELF?