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# What is the decimal expansion of an irrational number?

Updated: 4/28/2022

Wiki User

11y ago

A decimal expansion means to write out the base 10 digits of a number.

Because Irrational Numbers do not have a closed form, the decimal expansion will always be an approximation. Consider the irrational number pi, which has the following decimal expansion:

3.14159265...

Of course there are more digits to pi than that, which is denoted by the "...". It is sadly impossible to list ALL of the digits of an irrational numbers, since if there were a finite number of digits, you could express it as a fraction, which would not be irrational.

Wiki User

11y ago

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Q: What is the decimal expansion of an irrational number?
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### decimal expansion of irrational number is non terminating and?

The decimal expansion of an irrational number is non terminating and non recurring​

### What is the decimal expansion of an irrational no. is?

It is the decimal approximation to the value of the irrational number.

### 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 the decimal expansion of an irrational number is finite?

No. It must be infinite AND non-recurring.

### Is the square root of pi a rational or irrational number?

Pi, and the square root of pi, belong to a category known as transcendental numbers, which means that not only do they have an infinite decimal expansion (the numbers following the decimal go on forever) but the decimal expansion follows no pattern and is unpredictable. Irrational numbers also have an infinite decimal expansion, but not necessarily an unpredictable one.

### A decimal number is an irrational number?

A decimal number can be rational or irrational.

### Why does irrational numbers don't stop?

Because if they stopped they could be expressed as a ratio. Suppose the decimal expansion of an irrational stopped after x digit AFTER the decimal point. Now consider the number n, which is the original number, left and right of the decimal, but without the decimal point. This is the nummerator of your ratio. The denominator is 1 followed by x zeros. It is easy to show that this ratio repesents the decimal expansion of the number

### How doen you estimate an irrational number?

An irrational number has a never-ending decimal expansion. To estimate it's value, you'd just state the expansion to some number of digits. Ex: sqrt(2) is approximately 1.4142135623730950488 pi is approximately 3.14159265358979323846

### 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.

### How can you tell if a decimal is an irrational number?

When a decimal can't be expressed as a fraction then it is an irrational number.

### Is pi a recurring decimal a terminating decimal or an irrational number?

Pi is an irrational number

### What is the square root of number seven?

The square root of 7 is an irrational number, so its decimal expansion never ends and never repeats. Rounded to 3 decimal places it is 2.646.