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Rational numbershow is 0.333... a rational number?

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fadeela | Student, Grade 9 | eNotes Newbie

Posted November 4, 2011 at 3:47 AM via web

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Rational numbers

how is 0.333... a rational number?

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litteacher8 | Middle School Teacher | (Level 1) Distinguished Educator

Posted November 4, 2011 at 8:51 AM (Answer #2)

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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.

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fadeela | Student, Grade 9 | eNotes Newbie

Posted November 5, 2011 at 3:21 AM (Answer #3)

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What about non recurring/non repeating decimals? Are they rational or irrational?

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

Posted November 5, 2011 at 12:06 PM (Answer #4)

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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.

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matthew0109 | Student | (Level 1) Honors

Posted November 12, 2011 at 12:26 PM (Answer #5)

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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 .

 

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

Posted December 3, 2011 at 1:01 AM (Answer #6)

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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

 

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coolattitude | Student | eNotes Newbie

Posted May 4, 2012 at 3:59 PM (Answer #8)

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Rational numbers

how is 0.333... a rational number?

o.333 is a rational number as it is repeating

 

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