Is 0.3333.... a rational or irrational number?

Question

The 3s behind the decimal point are recurring. Since it can be expressed as a fraction but is never-ending, is it a rational or an irrational number?

Answer 1

Irrational, it beat up the number 5 with it's hand bag.

Answer 2

it's representation of 1/3 like 0.(3) and it's rational

Answer 3

Zero-point-repeating-three is a RATIOnal number because it can be represented as a ratio of two integers (two whole numbers).  It is equal to 1/3.

Answer 4

People just claiming that something is rational isn't very satisfying so I'll show you why it is.

Let x = 0.333333...

then 10*x = 3.33333....

10*x -x = 9*x = 3.0 {we just killed off the repeating decimal}

x = 3/9 or x = 1/3

So yes it is rational and that is why it is rational.

Answer 5

rational because it is a fraction of two integers ( 1/3 )

Answer 6

its irrational cuz its a reapeating decimal.

Answer 7

Rational! 'cos it can be presented as 1/3

Irrationals are pi, sqrt3 and so on

(they cannot be presented as such a fraction)

Answer 8

it is irrational in decimal form because it is repeating but if it is in fraction form it is rational

Answer 9

0.3333... is a rational number, because it can be represented by 1/3 (a ratio with two integers)

Answer 10

Rational, as it is 1/3. It can't be irrational, as irrational numbers can't be represented as a fraction

While it is not technically 1/3, it's the closest possible thing that COULD be 1/3.

Answer 11

RATIONAL NUMBER!!!!

　

　

　

cuz it can be also expressed as 1/3

　

　

Answer 12

.33333 (repeating) is a rational number. Even though it goes on forever it repeats a pattern and is therefore rational. Any decimal that repeats any pattern (however long) can be expressed as a finite fraction and is therefore considered rational

Answer 13

Rational because it can be written as 1/3. All fractions are rational. Pi and √2 are examples of irrational numbers because they cannot be written as a fraction with the exact same answer.

Pi can be written as 22/27 but 22/7 will not give the exact value of pi. It is just approximate. thus, it is irrational.

Answer 14

0.333.... is rational, but go much deeper to understand.

Answer 15

If a number cannot be expressed as a fraction (such is the case with surds) it is irrational. 0.333... is rational :)