Are all fractions rational numbers?


A rational number can be expressed in the form \displaystyle\frac{a}{b} where a and b are integers and b \neq 0. In other words, it is a fraction whose denominator is not zero, and both the denominator and numerator are integers.


Some fractions, however, may contain a numerator or denominator that is not an integer. Some examples of such fractions are

\displaystyle\frac{\sqrt{3}}{2}, \displaystyle\frac{\pi}{4} and \displaystyle\frac{e}{2}.

A rational number may be represented in many ways, but it can always be expressed as a fraction. For instance, 10^{-1} is a rational number because we can express it as \frac{1}{10}. Also, the number 0.333 \cdots, a repeating decimal, is  a rational number because we can also express it as fraction \frac{1}{3}.

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5 thoughts on “Are all fractions rational numbers?

  1. Actually, at Spain we usually call numbers as $\frac{\sqrt(3)}{2}$ ratios (razones), instead of fractions (fracciones). That way we can identify fractions and rational numbers. It’s just semantics, but it simplifies things a lot.

    • True. But, in English, we also have ratios containing integers, so that could be quite confusing. I’m glad it works in your country. 🙂

  2. is repeated no of infinite decimal no is irrational?pls say what is the difference between rational and irrational?

    • Hi Panju. Thank you for your comment. Infinite number of decimals (non-terminating decimals). can be rational or irrational. If a non-terminating decimal is repeating (e.g. 0.567567567… where 567 repeats infinitely), then it is rational. If the decimal is not non-terminating and non-repeating, then, it is irrational. To know more about rational and irrational numbers, please visit the link below.

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