Are all fractions rational numbers?

No.

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.

fractions

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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3 Comments

  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.

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

      Reply

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