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# How do you determine if a decimal is rational or not?

Updated: 10/19/2022

Wiki User

10y ago

A decimal is a rational number if it ever ends, or if it repeats

the same single digit or set of digits forever.

Wiki User

10y ago

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Q: How do you determine if a decimal is rational or not?
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### Is a repeating decimal rational or irrational?

A repeating decimal is rational.

### How do you change fractions to decimal and how to determine if it is rational or irrational?

To change a fraction to the equivalent decimal:Divide the top number by the bottom number.Regarding rational / irrational:Not to worry. Every fraction that you can write with numbers is rational,and so the equivalent decimal is too, even if it never ends.

### When A calculator is set to show up to 10 digits of a decimal number and yields the following 10 digit output .3263263263. Is it possible to determine whether or not this number is rational why?

The decimal shows a repeating pattern. Repeating decimals are rational.

### Is 4.101010001 a rational nummber?

It is rational because it is a terminating decimal

### Is 8.56909 a rational or irrational decimal?

Any terminating decimal is rational. So are repeating (periodic) decimals.Any terminating decimal is rational. So are repeating (periodic) decimals.Any terminating decimal is rational. So are repeating (periodic) decimals.Any terminating decimal is rational. So are repeating (periodic) decimals.

### A decimal that can be written into a fraction is called?

The decimal representation of a rational number.

### When a number is written in decimal and acirc and 128 and 139 form how do we know if the number is a rational and acirc and 128 and 139 number?

You cannot. There is no way to determine if the number has or has not been rounded and so no way to determine if the number is a terminating, repeating or other form of decimal number. Without that information you cannot tell if it is rational.

### Is 8.2 a rational number?

Yes. Any terminating decimal is a rational number. Any repeating decimal also.

### Is 0.454545... an irrational number?

No. It is a rational number. Any repeating decimal or terminating decimal is rational.

### 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.

### 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.

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