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Why is a recurring number rational?

Anonymous

∙ 14y ago

Updated: 4/28/2022

A recurring decimal can always be converted to a fraction with integer numerator and denominator, and that is precisely the definition of a rational number.

Example: let the recurring number be 0.3121212...

Call the number "x"

100x = 31.21212...

x = 0.31212...

Subtract the two equations:

99x = 30.9

990x = 309

x = 309/990

This can be simplified, but the point is that I converted the recurring decimal to a fraction, with integer numerator and denominator.

Wiki User

∙ 14y ago

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Q: Why is a recurring number rational?

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Is two thirds a rational number?

Yes, two thirds is a rational number. This is because it a is recurring decimal and can be expressed as a fraction. All fractions are rational numbers and all recurring decimals are rational numbers.

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Yes. Any terminating or non-terminating recurring decimal is a rational number.

Is - 0.29292929292929 a rational number or an irrational number?

Any terminating decimal or repeating decimal is a rational number.-0.29292929292929 iseither a terminating decimal of the fraction -29292929292929/100000000000000or meant to be a recurring decimal (0.2929...) with the '29' recurring forever of the fraction 29/99Either way, it is a rational number.

Is this a rational number 0.323232?

A rational number is a number that can be expressed as the division a/b where a and b are both integers. In this case 0.323232.... is a recurring decimal, and so is rational, as all recurring decimals are rational. This can be proved in the following way: 0.323232... x 100 = 32.323232... 0.323232... x 100 - 0.323232... = 32 0.323232... x 99 = 32 0.323232... = 32/99 Therefore 0.323232... is a rational number.

Is 0.58585858 a rational number or an irrational?

If that is a terminating decimal: 0.58585858 = 58585858/100000000 = 29292929/50000000 And thus a rational number If it's a recurring decimal: 0.58585858... = 58/99 And thus a rational number

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Related Questions

Is a recurring number an irrational number?

No, it is rational

Is non recurring rational number the same as terminating rational number?

Yes.

Is two thirds a rational number?

Yes, two thirds is a rational number. This is because it a is recurring decimal and can be expressed as a fraction. All fractions are rational numbers and all recurring decimals are rational numbers.

What is the difference between recurring and non recurring decimal?

A recurring decimal is a rational number, a non-recurring one may be rational (for example 0.2 = 1/5) or irrational.

Is 2.33333333333 a rational number?

Since 2.33333... is a repeating decimal (or recurring decimal), it is a rational number.

Why decimal is considered as rational number?

A decimal need not be a rational. A non-terminating, non recurring decimal is an irrational number. Only a terminating decimal or a recurring decimal is rational and that is because such a number can be expressed as a ratio of two integers.

Is decimal a rational number?

It depends. A terminating decimal is a rational number. A decimal which, after a finite number of places, becomes a repeating (or recurrent) decimal is also a rational number. A decimal that is not terminating, nor [eventually] settles into a recurring pattern is not a rational number. Note that the decimal need not become recurring immediately.

Is 6.121231234. a rational number?

Yes, it is. Any terminating or a non-terminating recurring decimal is a rational number. In this case, the decimal is terminated. And so, this number is a rational number.

Is 3.245245245 a rational number?

Assuming that the number ends at that third 5, yes, the number is rational - as it has a defined end-point. If the number is equal to 3.245 recurring, then no, the number will not be rational.

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If you mean recurring .... 6 then it is a rational number because it can be expressed as a fraction in the form of 1/6

Is 3.40764076407640764076 an rational number or irrational?

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