# Rational numbershow is 0.333... a rational number?

embizze | High School Teacher | (Level 1) Educator Emeritus

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If a number written in decimal form never repeats then it is irrational. e.g. the decimal expression for pi is an approximation since there is no repetition. All rational numbers have decimal expansions that either terminate (all remaining numbers are 0) or have a repeating sequence. Note that the entire decimal sequence need not repeat -- 1171/4950=0.236565656565... with the sequence 65 repeating indefinitely.

litteacher8 | High School Teacher | (Level 3) Distinguished Educator

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A rational number is any number that can be written as a ratio.  Think of a ratio kind of like a fraction, functionally at least.  For example, 0.33333 is a repeating decimal that comes from the ratio of 1 to 3, or 1/3.  Thus, it is a rational number.

coolattitude | Student | eNotes Newbie

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Rational numbers

how is 0.333... a rational number?

o.333 is a rational number as it is repeating

chrisbond437 | Student, Grade 10 | (Level 1) Honors

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A rational number can be written in the form:p/q, where q not equal to 0.

To represent 0.3333... as a fraction:

Let x=  0.3333...

=> 10x=3.33333...

=>10x-x=3.3333....-0.3333....

=>9x=3

=>x=1/3.

So we arrive that 0.33333...=1/3=rational number

matthew0109 | Student | (Level 1) Honors

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A rational number is any number that you can write in the form , where a and b are integers and b ≠(not equal to) 0. A rational number in decimal form is either terminating, such as 6.27, or repeating, such as8.222..., which you can write as . (a line is over the 2

All integers are rational numbers because you can write any integer n as .