powerpoint presentation

1. The Real Number System
Ms G. Martin

2. Real Numbers are the union of rational and
irrational numbers
Rational Numbers:
1. Natural / Counting numbers
2. Whole Numbers
3. Integers
4. Decimals
5. Fraction

3. The Set of Real Numbers
1. Natural Numbers (N)
The set of natural numbers is the first set that we have learned.
During our childhood days we are first taught by or parents/guardians
to count from one to ten. That set of numbers is the natural numbers
or counting numbers.
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …}

4. Examples:
• Natural numbers except 1, may either be prime or
composite.
The first 5 prime numbers = {2, 3, 5, 7, 11}
The first 5 composite numbers = {4, 6, 8, 9, 10, }

5. 2. Whole Numbers
The set of natural numbers is expanded to the set of whole
numbers. The set of whole numbers is the union of zero (0) and
natural numbers.
W = {0, 1, 2, 3, 4, 5, 6, …}

6. 3. Integers (Z)
Mathematicians created another set of numbers in order to
answer questions like “what is x if x + 10 = 5?” and “what is the
difference between 2 and 5?”
Integers comprise the set of negative integers and whole numbers.
Z = {…, -5, -4, -3, -2, -1,} ∪ {0} ∪ 1, 2, 3, 4, 5, …

7. There are different subsets of the set of integers. These are:
• The set of negative integers
Z = {… -5, -4, -3, -2, -1}
• The set of positive integers
N = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, …}
• The set of non-negative integers or the set of whole numbers
W = {0, 1, 2, 3, 4, 5, 6, …}
• The set of non-zero integers
Z = {…, -3, -2, -1, 1, 2, 3, …}

9. 4. Decimals
A decimal is a fraction that is written in the form of a dot
followed by one or more numbers which represent tenths,
hundredths, and so on.
5. Fraction
A fraction represents a part of a whole or, more generally, any
number of equal parts.

10. Rational Numbers (Q)
The set of rational numbers is a set of numbers that can be
expressed as a ratio/quotient of two integers where the divisor is not
zero. If a and b are integers and b ≠ 0, then
𝑎
𝑏
is a rational number.
Every rational number can be written in fraction and decimal
form. Rational numbers in fraction form can be written in decimal
form and rational numbers in decimal form can be renamed in
fraction form.

11. Rational numbers include natural numbers, whole numbers, and
integers. They can all be written as fractions. Sixteen is natural, whole, and
an integer. Since it can also be written as the ratio 16:1 or the fraction 16/1,
it is also a rational number.
Examples:
1.
𝟏
𝟕
5. 10 =
𝟏𝟎
𝟏
2.
𝟑
𝟔
6. -2 =
−𝟐
𝟏
3. 0.25 =
𝟏
𝟒
7. 0 =
𝟎
𝟏
4.
𝟕
𝟏𝟎
= 0.35 8. 15 =
𝟏𝟓
𝟏

12. Thank You!
SMSDGRADE7-MT. EVERES
@ODL2020