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What are the two possibilities for the decimal expansion of a rational number?
Wiki User
∙ 8y ago
It terminates or has a infinite repeating expression.
Wiki User
∙ 6y ago
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What can you say about the decimal expansion of any rational number?
If its a rational number then its decimal equivalent can be expressed as a fraction
What is the difference between the decimal expansion in irrational and rational numbers?
Decimals that terminate or repeat in some fashion are rational, while decimals that expand forever are irrational.
Is 7.148714289.. rational?
The answer to the question depends on exactly how the decimal expansion proceeds. If it is non-repeating, then the number is not rational.
Is 5 over 2 an irrational number?
No, actually 2/5 is equal to .4 which is perfectly rational. Irrational numbers have an infinitely long decimal expansion. This is just one digit. Any rational number divided by any other rational number gives another rational number. Having an infinitely long decimal expansion is a necessary but not sufficient criterion for irrationality... for example, 1/3 is rational, though its decimal expansion is the infinitely long 0.33333333...
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.
What can you say about the decimal expansion of any rational number?
If its a rational number then its decimal equivalent can be expressed as a fraction
Is a number with an unending decimal expansion irrational?
No. If the decimal expansion falls into a repeating pattern (however long) then the number is rational. For example, 0.33... is the rational number 1/3. or 0.04142857142857... where the pattern 142857 continues forever is the rational number 29/700.
What is the difference between the decimal expansion in irrational and rational numbers?
Decimals that terminate or repeat in some fashion are rational, while decimals that expand forever are irrational.
Is 7.148714289.. rational?
The answer to the question depends on exactly how the decimal expansion proceeds. If it is non-repeating, then the number is not rational.
Is 5 over 2 an irrational number?
No, actually 2/5 is equal to .4 which is perfectly rational. Irrational numbers have an infinitely long decimal expansion. This is just one digit. Any rational number divided by any other rational number gives another rational number. Having an infinitely long decimal expansion is a necessary but not sufficient criterion for irrationality... for example, 1/3 is rational, though its decimal expansion is the infinitely long 0.33333333...
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 8.2 a rational number?
Yes. Any terminating decimal is a rational number. Any repeating decimal also.
is 0.313111331 a rational or irrational number?
It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational.
Is 0.454545... an irrational number?
No. It is a rational number. Any repeating decimal or terminating decimal is rational.
Is one over nine rational?
yes, 1/9 is a rational number, also written as .11111111111111...Even though the decimal expansion is infinite, it is also a recognizable pattern, and hence rational.
When a number is written in decimal form how can you tell if it's a rational number?
We know that a real number is rational if and only if, when expressed as a decimal, it has a finite or recurring expansion. . . (put a point exactly over 8 and 2). For example, 5/4 = 1.25, 2/3 = 0.6, 20/7 = 2.857142857 or 20/7 = 2.857142
is 27.5 rational or irrational?
It is rational. An irrational number is a number that you cannot define by a fraction or a decimal. Since you wrote it as a decimal, it is rational.
