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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.

Q: What is the decimal expansion of an irrational number?

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No. If you write an irrational number as a decimal, it will have an infinite number of decimal digits that don't repeat periodically.

No, this is a rational number.It is 975,441,317/312,500,000.In general, any number which has a decimal representation that either terminates (ends after some finite length) or repeats is a rational number (not an irrational one). Because this decimal expansion terminates, it is a rational number.However, there are an infinite number of irrational numbers which begin with 3.1214122144.... Generally, we notate the approximation with the ellipses (...) and know we cannot record in a decimal form its exact value.NAOMI WAS HERE

It is rational.A number cannot be both rational and irrational.

It is non-terminating decimal and therefore it is an irrational number

No. A rational number is any terminating numeral. A repeating decimal is irrational.

Related questions

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

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

Decimals that terminate or repeat in some fashion are rational, while decimals that expand forever are irrational.

No. It must be infinite AND non-recurring.

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 can be rational or irrational.

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

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

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.

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

Pi is an irrational number

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.