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No, all terminal decimals are rational numbers. For a number to be irrational, its decimal representation must be non-terminal (never end) and never repeat. Here are a few terminal decimals and their fractional equivalents. Note that any number which can be expressed as any ratio of integers is rational.

0.333 = 333/1000

0.4 = 4/10 = 2/5

0.1427 = 1427/10000

In general, any terminating decimal expression has a certain number of digits after the decimal point. We will call those digits D1, D2, D3, D4, ... DN. We will ignore the whole-integer part of the number as this is rational and any rational number combined with another rational number is rational. The non-integer part (fractional-part) of this number can be expressed as the ratio:


The numerator is an integer because all of the Dxs are integers from 0 to 9 inclusive. The denominator is an integer because N is the number of digits after the decimal in the terminal decimal expression, and 10 to a finite, integer power is an integer. Thus, any terminating decimal can be expressed as a ratio of two integers and is thus rational (not irrational).

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Irrational Numbers are non-terminating decimals.

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Q: Are terminal decimals irrational numbers
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Related questions

Are repeating decimals rational?

Yes. Rational numbers are numbers or decimals that repeat or terminate. Irrational numbers do not. For example π is an irrational number.

Are recurring decimals considered irrational numbers?

No. Recurring decimals are rational numbers.

Are terminating and repeating decimals irrational numbers?

Terminating and repeating decimals are rational numbers.

Can negative decimals be irrational numbers?


What are terminating and repeating decimals?

Irrational Numbers.

Are decimals irrational or rational numbers?

They can be both

Are repeating decimals rational or irrational numbers?

Repeating decimals are rational numbers if there is a pattern, like 0.22222222. If it is not a pattern, like 0.568964329, it is an irrational number.

What type of decimals are irrational numbers?

Non-terminating, non-repeating decimals.

Why cant irrational numbers be represented in decimal form?

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

Numbers that cannot be expressed as terminating or repeating decimals?

irrational numbers

Are all integer irrational numbers?

No integers are irrational numbers. An integer is a whole number, positive or negative. This means they have no decimals or fractions. An irrational number, however, is a number with fractions or decimals. Therefor, there are no integers that are irrational numbers.

What do you called the set of infinite decimals and non perfect square root?

Infinite decimals: irrational numbers; Non-perfect square roots: a subset of irrational numbers.