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Converting Fractions (continued)


fractions with the number 2, 5, 10 or their multiples in the denominator ARE decimal fractions


  1. Because you can convert them into decimal fractions: 23/400=23/(4x100)=(23/100)X1/4=23/100 x 25/100= 575/10'000
  2. Because 2 x 5 = 10
  3. Because 2, 5 are prime numbers
  4. Because you can transform 25 into 100, and so, for example 2/25 = 8/100
  5. because you can transform 5 into 10, and so for example 3/5 = 6/10
    (do you remember equivalent fractions?)

And so on...

For further understanding, here is a picture to summarize fractions and decimals relationships.

fractions and decimals recap chart


So here is the aswer for

"Is a decimal fraction always finite?"

"Is a non decimal fraction alway finite?"








Leonardo in his famous Codice Atlantico, makes quite many mistakes with fractions [1], so don't despair!

Here is a first example (foglio 191 v.)

Leonardo Da Vinci mistake with fractions

And again (foglio 665 r.) Leonardo writes:

Leonardo Da Vinci mistake with fractions, second example

I stop here (there are more mistakes he made).

...Our modern power of easy reckoning
with decimal fractions is the most miraculous result of a perfect

Introduction to Mathematics (New York,

1911), p. 59.


...All through your work as teachers you will
bear in mind the fundamental difference between knowing and
thinking; and will feel how much more important relatively to
the health of the intellectual life the habit of thinking is than
the power of knowing, or even facility of achieving visible re-
sults. But here this principle has special significance. It is by
Arithmetic more than by any other subject in the school course
that the art of thinking consecutively, closely, logically can
be effectually taught. FITCH, J. G.

Lectures on Teaching (New York, 1906),


Source: Memorabilia mathematica; or, The philomath's quotation-book - Moritz, Robert Édouard, 1868-1940





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