® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)
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Transcript of ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)
![Page 1: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/1.jpg)
® Ramziah AL Kaissi
REAL NUMBERS
(as opposed to fake numbers?)
![Page 2: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/2.jpg)
® Ramziah AL Kaissi
Natural Numbers• Are the set of
counting numbers.
• Example:{1, 2, 3,…}
Zero is not a natural number
![Page 3: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/3.jpg)
® Ramziah AL Kaissi
Whole Numbers:
Whole numbers are the same as the natural number. The only difference is that whole numbers include the number zero.
All Natural Numbers are Whole Numbers.
W
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® Ramziah AL Kaissi
Integers
• Include all positive whole numbers, negative whole numbers and zero
• Example {…,-3, -2, -1, 0, 1, 2, 3,…}
![Page 5: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/5.jpg)
® Ramziah AL Kaissi
All Natural Numbers are Integers.
• Natural numbers is subset of the Whole Numbers.
• Whole Numbers is subset of Integers.
Natural Number is subset of Integers
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® Ramziah AL Kaissi
Examples of Integers
6-120186-934
Integers
Whole Numbers Natural
![Page 7: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/7.jpg)
® Ramziah AL Kaissi
Rational Numbers
• Can be written as a ratio of two integers.
• e.g.:
• Can be written in decimal form is terminating or repeating.
b
a
9
4
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® Ramziah AL Kaissi
Terminating Decimal:
Are decimals that contain a finite number of digits.• Examples:
36.8 = 368/100.125= 125/10004.5= 45/10
Terminating Decimals are Rational Numbers because they can be written as fractions
![Page 9: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/9.jpg)
® Ramziah AL Kaissi
Repeating Decimal:
Are decimals that contain an infinite number of digits.Examples: 0.333… , 7.689689…
Repeating Decimals are Rational Numbers because they can be written as fractions
![Page 10: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/10.jpg)
® Ramziah AL Kaissi
Examples of Rational Numbers
• 16• 1/2• 3.56
• -8• 1.3333…• - 3/4
Rational Numbers
Integers Whole Numbers Natural
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® Ramziah AL Kaissi
All Natural Numbers and All Integers are Rational Numbers• Natural numbers is one subset of the Rational Numbers.
• Integers are another subset of Rational Numbers.
• Whole Numbers is another subset of Rational Numbers.
![Page 12: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/12.jpg)
® Ramziah AL Kaissi
All Natural Numbers and All Integers are Rational NumbersNatural numbers, whole numbers and integers are Rational numbers because you can write them as a fraction
1
189189
1
33
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® Ramziah AL Kaissi
Irrational Numbers• Irrational numbers are any numbers that
cannot be expressed as fractions (ratio of two integers) .
• They are expressed as non-terminating, non-repeating decimals; decimals that go on forever without repeating a pattern.
• Examples of irrational numbers:• 0.34334333433334…• 45.86745893…• (pi) = 3.14…•
I
2
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® Ramziah AL Kaissi
Real Numbers
Irrational Numbers
I&
Rational Numbers
![Page 15: ® Ramziah AL Kaissi REAL NUMBERS (as opposed to fake numbers?)](https://reader035.fdocuments.us/reader035/viewer/2022062315/5697bfcf1a28abf838ca9def/html5/thumbnails/15.jpg)
® Ramziah AL Kaissi
SummaryReal Numbers
Rational Numbers
Integers
Whole Numbers
Natural
Irrational Numbers