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# Are terminal decimals irrational numbers

Updated: 4/28/2022

Wiki User

12y ago

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:

(D1D2D3...DN)/(10N)

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).

Wiki User

12y ago

Wiki User

11y ago

No.

Irrational Numbers are non-terminating decimals.

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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 &pi; 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.

Yes.

### What are terminating and repeating decimals?

Irrational 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.