The document reviews different types of numbers including natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. It also discusses converting between decimals and fractions. Key points covered include the different types of numbers, comparing types of numbers using a visualization of concentric circles, determining which number type a given number belongs to, and the steps for converting decimals to fractions and fractions to decimals. Students are encouraged to ask the teacher or contact the presenter if any areas are unclear or difficult to understand.

1. Number Types
(and fractions and decimals)

2. The lesson you just studied is fairly comprehensive.
Rather than repeat the lesson, the purpose of this presentation is to review major
points with the hope of adding clarity in certain areas.
Points to review include:
• types of numbers.
• converting decimals to fractions, and
• converting fractions to decimals,
You may find that other areas were difficult to grasp. If that is the case, don’t
hesitate to talk to Mrs. Kent or to contact me in the evenings.

3. Types of Numbers
› Natural Numbers: numbers “naturally” used for counting:
1, 2, 3, . . .
› Whole Numbers: the Natural Numbers and zero: 0, 1, 2, 3, . . .
› Integers: the Natural Numbers, their opposites, and zero: .
. ., -3, -2, -1, 0, 1, 2, 3, . . .

4. Types of Numbers

5. Types of Numbers
› Irrational Numbers: any number that isn’t rational. An irrational
number can only be approximated as a decimal value because
it never repeats and it never terminates (e.g. the square root of
a prime number).
› Real Numbers: all numbers on the number line.

6. Types of Numbers
Natural Numbers
(counting numbers)
1, 2, 3, . . .
Whole Numbers
0, 1, 2, 3, . . .
Integers
. . ., -3, -2, -1, 0, 1, 2, 3, . . .
Real
Numbers

7. A Useful Comparison
San Antonio
Texas
The United States
North America
Asia
The World

8. Types of Numbers
Is a person in San Antonio also in Texas?
Yes, always.
Is a person in Texas also in San Antonio?
Maybe, but not necessarily.
Is a Natural Number also a Whole Number?
Yes, always.
Is a Whole Number also a Natural Number?
Maybe, but not necessarily.

9. Types of Numbers
Is a person in North America also in the USA?
Maybe, but not necessarily.
If a person in the USA in San Antonio?
Yes, always.
Is a Rational Number also an Integer?
Maybe, but not necessarily.
Is an Integer also a Rational Number?
Yes, always.

10. Types of Numbers
So, as indicated, anyone in one circle is
automatically in all those around/above it.
If a person is in Texas (but not San Antonio),
that person is also in the USA, North America,
and, of course, the world.
So, as indicated, any number that’s one type is
automatically in all those around/above it.
If a number is a Whole Number, that number is
also an Integer, a Rational Number, and, of
course, a Real Number.

11. Determining Which Number Type
See if you agree:
Natural Number          
Whole Number          
Integer          
Rational Number          
Irrational Number          
Real Number          

12. Converting Decimals to Fractions

13. Converting Decimals to Fractions

14. Converting Decimals to Fractions
› Steps for non-terminating, non-repeating decimals
› Determine how many places are sufficient and round
› Handle as you would a terminating decimal

15. Converting Fractions to Decimals
0.
7 3
2 8
20
14
60
56
40
35
50
49
10
7
30
28
*Your teacher will tell you how many places “close enough” is. Often it will be just 2 or 3, but
sometimes, your teacher will want you to continue to see if there’s a pattern.
Do you see the pattern here?
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