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Rational and Irrational Numbers: Understanding the Difference, Lecture notes of Calculus

An introduction to rational and irrational numbers, including examples and the difference between the two. Rational numbers are those that can be written as a fraction of integers, while irrational numbers cannot. How to identify rational numbers by looking for terminating or repeating decimals.

What you will learn

  • How can you identify a rational number?
  • What are irrational numbers and how do they differ from rational numbers?
  • What are rational numbers?

Typology: Lecture notes

2021/2022

Uploaded on 09/12/2022

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Rational Numbers
The rational numbers make up the set of all numbers that can be written as a
fraction of integers. In other words, any time you see an integer divided by
another integer, you’re looking at a rational number.
Examples of Rational Numbers
2/5 3/8 7,000 (since 7,000/1 = 7,000)
4 (since 4/1 = 4) .673 0
-.7
Which of the following are rational numbers?
1. 2/7
2. 0/5
3. -12
4. .137
5. -.64
pf2

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Rational Numbers

The rational numbers make up the set of all numbers that can be written as a fraction of integers. In other words, any time you see an integer divided by another integer, you’re looking at a rational number. Examples of Rational Numbers 2/5 3/8 7,000 (since 7,000/1 = 7,000) 4 (since 4/1 = 4) .673 0

-.

Which of the following are rational numbers?

Irrational Numbers

The irrational numbers make up the set of all numbers that cannot be written as a fraction of integers. Examples of Irrational Numbers

The way to tell a rational number from an irrational number is to

look at the number when it is written in decimal form.

Here’s the rule:

The decimal form of a rational number has only two choices in life:

it can either terminate, meaning it ends

or it goes on forever

On the other hand the irrational form of a number does neither of

these things.

Difference between rational and irrational numbers

  1. Rational number: 7/8 = .875 the decimal terminates
  2. Rational number: 4/11 = .363636… The decimal repeats in a regular pattern.
  3. Irrational number: 3 = 1.732058 This decimal goes on and on in a pattern no human being has ever made sense of.