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 $\frac{1}{3}$ .

3 comments on “Are all fractions rational numbers?”

JJ on January 6, 2013 at 8:26 pm said:

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.

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Guillermo Bautista on January 7, 2013 at 4:43 pm said:

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

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