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Both rational and Irrational Numbers can be expressed with decimals. If the number is irrational, it will have an infinite number of decimal digits, and there will be no periodic repetition. For example, 1/7 (which is rational) is 0.142857 142857 142857... The same sequence of six digits repeats over and over again. In irrational numbers, this is not the case.

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Q: Are irrational numbers always decimal numbers?

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Decimal numbers that can't be expressed as fractions are irrational numbers

They are the decimal numbers that can't be expressed as fractions.

No, irrational numbers can't be expressed as a terminating decimal.

All irrational numbers have decimal representations which are non-terminating.

Irrational numbers are numbers that cannot be expressed as a ratio of two integers or as a repeating or terminating decimal.

But irrational numbers are decimals that can't be expressed as fractions

No, numbers less than 0.833 are not always irrational. For instance, 0.2 isn't an irrational number

Irrational numbers are decimal numbers that can't be expressed as fractions. An example is the square root of 2

The difference is that rational numbers stay with the same numbers. Like the decimal 1.247247247247... While an irrational number is continuous but does not keep the same numbers. Like the decimal 1.123456789...

Irrational numbers can't be expressed as fractions Irrational numbers are never ending decimal numbers The square root of 2 and the value of pi in a circle are examples of irrational numbers

Decimal numbers that can be expressed as fractions are rational but decimal numbers that can't be expressed as factions are irrational

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.

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