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Understanding Rational and Irrational Numbers: Identification and Examples, Summaries of Calculus

An overview of rational and irrational numbers, their characteristics, and examples. Rational numbers are those that can be expressed as fractions, while irrational numbers cannot. examples of both types of numbers and explains their significance on the number line.

What you will learn

  • What is the definition of a rational number?
  • Can you provide examples of irrational numbers?
  • How do rational and irrational numbers differ on the number line?
  • Can you provide examples of rational numbers?
  • What is the definition of an irrational number?

Typology: Summaries

2021/2022

Uploaded on 09/12/2022

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Rational
and
Irrational Numbers
Learning Target:
Students can identify numbers as being
rational or irrational.
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Rational

and

Irrational Numbers

Learning Target:

Students can identify numbers as being

rational or irrational.

All REAL numbers are

made up of

RATIONAL & IRRATIONAL

numbers…

Examples of Rational Numbers

Fractions

Terminating Decimals

(stop / end)

Repeating Decimals

(decimal goes on forever)

Whole Numbers

Perfect Squares

Rational Numbers

are “Nice & Neat!”

2

3

− 9

2

1

1

4

  • 6.23 17.
  1. 23 − 621. 5

1 , 267

− 6 3

9 100 400

Irrational Numbers

All numbers that are not rational are considered irrational.

An irrational number can be written as a decimal, but not as

a fraction.

Irrational numbers can NOT

be written as a fraction!!

Pi is a famous irrational number. People have

calculated Pi to over a quadrillion decimal places

and still there is no pattern. The first few digits look

like this:

3.1415926535897932384626433832795…

The number e (Euler’s Number) is another famous

irrational number. People have also calculated e to

lots of decimal places without any pattern showing.

The first few digits look like this:

2.7182818284590452353602874713527…

The Golden Ratio is an irrational number.

The first few digits look like this:

1.61803398874989484820...

Both rational and irrational numbers show up on

the number line. This is why all “REAL” numbers

include rational and irrational numbers.

Non-Real Numbers

Imaginary Numbers:

If there is a negative inside the radical, then it is a

NON-REAL NUMBER

Radicals can’t
have a negative
number
(only +𝒙 )

Infinity:

Infinity is the idea of something that has no end.

These are ok (the negative is outside of the radical)