Classifying Numbers

Rational Numbers vs. Irrational Numbers

2

A Rational Number:

• Can be written as a simple fraction in the form

• p and q are integers• q can not equal 0• Can be a repeating

decimal such as 1.333 . . .

(can be written as 4/3)

An Irrational Number:

• Cannot be written as a simple fraction

• Non-terminating decimal (doesn’t end)• Non-repeating decimal (doesn’t repeat in a pattern)

Irrational doesn’t mean that it’s crazy!

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Examples of Rational Numbers

Click on each number to see explanation

Can be written as

3/1

3

.111 . . .

.007

-1/4

1.5

Can be written as

3/2

Can be written as 7/1000

Repeating decimal. Can be written as

1/9

Already in fraction form

√𝟏𝟔

Can be written as 4 and as 4/1

4

Examples of Irrational Numbers

is a famous irrational number.

= 3.141592653589 . . . It is irrational because it cannot be

written as a fraction.Popular approximations of are

3.14 or 22/7 They are close but not exactly

equal to .

5

More Irrational NumbersClick on each number to see explanation

Remember . . .Irrational numbers are non-repeating and non-

terminating decimals and cannot be written as a fraction.

= 1.414213. . . Can’t be written as

a fraction

√𝟐

.193045...

-32.47907…

e

√𝟗𝟗

= 9.98947. . . Can’t be written

as a fraction

Non-repeating decimal. Can’t be written as a

fraction

Non-repeating decimal. Can’t be written as

fraction

Natural base e = 2.7182818 . .

A mathematical constant like

6

Try this . . .Enter in your calculator.

It equals 13, which can be written as 13/1. is a RATIONAL NUMBER

169 is called a PERFECT SQUARE,

a whole number that is the result of another whole number squared.

Now enter in your calculator. Does it end? Of course it does because calculator screens can’t go on forever.

It equals approximately 12.84523258 , but would go on forever if possible. A square root of any number that is

not a perfect square is an irrational number.165 is NOT A PERFECT SQUARE and so

is IRRATIONAL.

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Time to practice

0.5 is . . .

⃝" Irrational

⃝" Rational

INCORRECT0.5 can be written as ½ and so it is rational.

Try again!

Correct!0.5 can be written as

½ Good work!

X

X

8

Time to practice

is . . .

⃝" Irrational

⃝" Rational

INCORRECT is equal to 7 and can be written as 7/1.

Try again!

CORRECT! is equal to 7 and can be written as

7/1.

X

X

9

Time to practice

-5.060715… is . . .

⃝" Irrational

⃝" Rational

CORRECT!-5.060715…

non-repeating, non-terminating decimal

Good job!

INCORRECT-5.060715… appears

to be a non-repeating, non-

terminating decimalTry again!

X

X

10

Time to practice

is . . .

⃝" Irrational

⃝" Rational

CORRECT! = 9.05538…

Non-repeating, non-terminating decimal.

Awesome!

INCORRECT = 9.05538…

Can’t be written as a fraction.

Try again!

X

X

11

Time to practice

2/3 is . . .

⃝" Irrational

⃝" Rational

INCORRECT2/3 is a fraction and

so it is rational.Try again!

CORRECT2/3 is a fraction.

Good work!

X

X

12

Time to practice

is . . .

⃝" Irrational

⃝" Rational

CORRECT ! = 3.31662 . . .

Can’t be written as a fraction. Nice job!

INCORRECT = 3.31662 . . .

Can’t be written as a fraction.Try again!

X

X

13

How many RATIONAL numbers can you find?

-2.357.143790…

√𝟔𝟒0

√𝟏

√𝟏𝟒𝟒√𝟓

√𝟐𝟕𝝅

Find the answer on the next slide

14

Did you find 6 rational numbers?

They are: 0

-2.35

Nice Work!