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Just by semantics alone, would you consider it a fraction when it is not written in a 'fractional' format?

lawonga
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  • What is your definition of fraction? Does it refer to the notation or to whether the value is rational? – Ross Millikan May 18 '18 at 03:43
  • I think it's pretty standard usage for "fraction" to mean the representation of the number and not the number itself. However, it can at times mean the number itself. – Cheerful Parsnip May 18 '18 at 03:44
  • I'm wondering under the standard, widely believed definition of a fraction, is a number such as 0.233 a fraction. – lawonga May 18 '18 at 03:45
  • Just trying to win an argument with someone else, actually, but I'd like to know too! – lawonga May 18 '18 at 03:45
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    Good luck finding a standard, widely believed definition that is not contradicted by some other standard, widely believed definition. – David K May 18 '18 at 03:47
  • 0.345 is a rational number, which means that it can be represented as a fraction. i.e. $\frac {345}{1000}.$ I would say the number 0.345 is not a fraction if it is not represented as one. – Doug M May 18 '18 at 04:02
  • The Oxford English Dictionary defines decimal fraction as "a fraction whose denominator is a power of ten (e.g. 5/100); (in later use also) such a fraction expressed as a decimal (e.g. 0.05)" so I would say yes. – bof May 18 '18 at 04:09
  • $0.345$ denotes the fraction $345/1000$. – Angina Seng May 18 '18 at 04:25

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As others have pointed out in the comments, there may be contradictory definitions, and it depends on what the context is.

That being said, have a look at the description of the tag you used for the question:

(fractions): Questions on fractions, i.e. expressions (not values) of the form $\frac ab$, including arithmetic with fractions. Not to be confused with the tag (rational-numbers): fractions denote rational numbers, but the same rational number may be written in different ways as a fraction.

So $0.345$ is definitely a rational number, but in its current form is not a fraction according to this description.

Théophile
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