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Understanding Rational Numbers: Fractions, Whole Numbers, Integers, and Decimals, Lecture notes of Calculus

An introduction to rational numbers, explaining what they are, their different forms as fractions, whole numbers, and decimals. It covers terminating and repeating decimals, and includes examples and exercises for testing whether numbers are rational or not.

What you will learn

  • How can natural numbers be written as rational numbers?
  • What is the difference between terminating and repeating decimals in rational numbers?
  • What are rational numbers?

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

geryle
geryle 🇺🇸

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NOTES&'RATIONAL'NUMBERS''''Date'___________________'
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RATIONAL(NUMBERS'are'numbers'that'can'be'expressed'as'
fractions.'This'includes'natural'numbers,'whole'numbers'and'
integers.'
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If'a'number'is'not'rational,'it'is'an'IRRATIONAL(NUMBER.'
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Natural'numbers'(counting'numbers)'{1,'2,'3,'4…}'
(Zero(is(NOT(included(in(the(natural(numbers.(
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Whole'numbers''All'natural'numbers'and'zero.'
' ' {0,'1,'2,'3,'4…}'
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Integers''All'whole'numbers'and'their'opposites.'
' ' {…'&3,'&2,'&1,'0,'1,'2,'3…}'
'
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Download Understanding Rational Numbers: Fractions, Whole Numbers, Integers, and Decimals and more Lecture notes Calculus in PDF only on Docsity!

NOTES-­‐ RATIONAL NUMBERS Date ___________________ RATIONAL NUMBERS are numbers that can be expressed as fractions. This includes natural numbers, whole numbers and integers. If a number is not rational, it is an IRRATIONAL NUMBER. Natural numbers (counting numbers) {1, 2, 3, 4…} Zero is NOT included in the natural numbers. Whole numbers  All natural numbers and zero. {0, 1, 2, 3, 4…} Integers  All whole numbers and their opposites. {… -­‐3, -­‐2, -­‐1, 0, 1, 2, 3…}

Rational numbers as a fraction Any rational number can be written as a ratio of two numbers, in the form where a and b are integers and b is not zero. Rational numbers as a whole number Any integer can be written as a rational number! How? 43 -­‐ 12

Non terminating, non repeating decimals ARE NOT rational numbers. π = 3.14159265… 0.5480390857… Testing whether a decimal is terminating or repeating: EXAMPLE 1: Write 5/8 as a decimal. EXAMPLE 2: Write 7/12 as a decimal.

Testing Square Roots: means the number that multiplied by itself gives you 81. Since 9 9 = 81, = 9. is a rational number. means the number that multiplied by itself gives you 40.  too low  too high Since no whole number works, is NOT a rational number.