Is this number rational or irrational?

Question

1.001001001...

Is it rational or irrational and why?

Answer 1

Rational. All numbers with repeating decimals are rational.

Answer 2

If a number ends with an infinitely repeating finite pattern of digits after the decimal point, it can be represented as a fraction.

If you think about turning a fraction into a decimal (dividing the denominator into the numerator using long division), the repeated pattern represents a repeated loop of remainders.

For info, 1.001001001.... is 1 1/999.

Edit: in response to capwest5a's answer. 1 / 0.999 can be rewritten as 1000 / 999, where both are integers. You could take any rational number and force into a ratio of two non-integers (e.g. 0.5 = 1/2 = 1.5 / 0.75), but that doesn't stop it being rational. Irrational numbers are things like sqrt 2, which cannot be written as the ratio of two integers.

Answer 3

I think it's rational because it has a repeating pattern (.001001001)

Answer 4

Oops! My bad! lol ty for pointing out my error!


I disagree with the first answerer.

A rational number is a number which can be expressed as a ratio of two INTEGERS.

1 / 0.999 = 1.001001001 . . .

0.999 is not an integer

Answer 5

rational (repeating number)

Answer 6

rational . . . . .. can be express as a fraction
1.001001001 . . .
= 1000/999

Answer 7

It's rational
It has repeating decimals.

pi can be expressed as a fraction but it is irrational
example:
pi/2, pi/3, pi/4 etc.

not every decimal is rational.
pi = 3.14159 etc.but never repeats.

Answer 8

rational. every decimal number is rational