Lesson-1-Real-Numbers.pdf real numbers , real number

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1. CALCULUS 1
W/
ANALYTICAL GEOMETRY
LESSON 1
M 106

2. REAL NUMBERS
LESSON1

3. 3
Bytheendofthissection,youwillbeableto:
•Convertbetweendecimalsandfractions;
•Writeinequalities;
•Applythebasicpropertiesofalgebra;
•Workwithexponentsandscientificnotation;and
•Interpretinequalitiesusingthenumberline.

4. REAL NUMBERS
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5. REAL NUMBERS
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6. REAL NUMBERS
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7. REAL NUMBERS
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8. REAL NUMBERS
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9. REAL NUMBERS
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10. REAL NUMBERS
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11. EXERCISES
11
Direction: Identify the following numbers; write Rif the number is Rational and IRif it’s
Irrational.
Moreover, if it is rational, simplify if it is an Integer
1.) 0.3564603
2.) 5
3.) 3/5
4.) 1.222222
5.) 0/35
6.) -356
7.) 2
8.) 9
9.) 8.969696
10.) 5/0

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REVIEW!

14. Therealnumbersystemisacomprehensive
mathematicalconstructthatencompassesall
possiblenumbersusedinmathematicsand
everydaylife.Itincludesrationalnumbers,irrational
numbers,integers,wholenumbers,andnatural
numbers.Therealnumbersareoftendepictedona
numberline,whereeachpointcorrespondstoa
specificrealnumber.

15. Here's a breakdown of the different components of
the real number system:
1. Natural Numbers (N): These are the counting numbers that begin
from 1 and go on infinitely: 1, 2, 3, 4, ...
2. Whole Numbers (W): These are similar to natural numbers, but
they also include zero: 0, 1, 2, 3, ...

16. 3. Integers (Z): Integers are the set of all positive and negative
whole numbers, including zero: ..., -3, -2, -1, 0, 1, 2, 3, ...
4. Rational Numbers (Q): Rational numbers are those that can be
expressed as fractions, where the numerator and denominator are
integers and the denominator is not zero. Examples include 1221,
−34−43, 5115.

17. 1.)
1
2
Tell whether the given is Rational, Irrational, Integers
Rational
2.) ??????
Irrational
3.) 0.333..
Rational
4.) 4 Integer
5.) 0 Integer

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✓Interval notation is a way of representing a range of
values on the real number line using brackets and
parentheses.
✓There are four main types of intervals: open intervals,
closed intervals, half-open intervals, and unbounded
intervals.

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1.Open Interval: (a, b)
Interval Notation: (2, 6)
Graph:
2. Closed Interval:[a, b]
Interval Notation: [−3, 1]
Graph:
───●───●───●───●───●───
-3 -2 -1 0 1
───●───●───●───●───
2 3 4 5 6
( ●
(
[ ]
3.a. Half-Open Interval (Open on One End, Closed on the Other): [a, b)
Interval Notation: [0, 4)
Graph:
───●───●───●───●───
0 1 2 3 4
●[
(
Four main types of intervals

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( ●
(
]───●───●───●───●───
-∞ -1 0 1 2
3.b. Half-Open Interval (Closed on One End, Open on the Other): (a, b]
Interval Notation: (−∞, 2]
Graph
4. Unbounded Interval: (-∞, ∞)
Interval Notation: (-∞, ∞)
Graph:
───────────────────────
-∞ ∞
(

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1.Edwards,R.L.B.(2015).Calculus.10
th
edition.CengageLearningAsiaPteLtd.
2.https://www.pdfdrive.com/calculus-early-transcendental-functions-fourth-edition-
e156660862.html
3.https://www.pdfdrive.com/calculus-early-transcendentals-e158296776.html
4.https://www.pdfdrive.com/calculus-early-transcendentals-e158302999.html
5.https://www.pdfdrive.com/contemporary-pre-calculus-textbook-e21032380.html
6.https://www.pdfdrive.com/multivariable-calculus-with-applications-e158268391.html
7.https://www.pdfdrive.com/calculus-early-transcendentals-10th-edition-d52069751.htm