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Converting Fractions

Converting fractions is the key to understand a little more about fractions and decimals.

Fractions ARE decimals! But it's not bad if you haven't realized this yet.

Decimals were developed about 400 years ago because it had been always too complicated to perform calculations with just fractions (which were then called "broken numbers"). It took 4500 years to humankind for the passage from fractions to decimals!The ancient Egyptians, Greeks, Babilonians, Mayans, Aztecs, Chinese,Romans would be astonished to see what pupils can calculate today!

Fractions can be subdivided into two large groups:

  • decimal fractions
  • NON- decimal fractions.

Remember: a decimal fraction is fraction like 5/10, 34/1000, 24678/10000 where 10 or its powers (10, 100, 1'000, 10'000, etc..) are present as denominator (the part below the fraction).

The following important questions arise:

is a decimal fraction always finite?

is a NON decimal fraction alway finite?


Try to look at these questions on your own, use a calculator and perform the division of fractions above(5/10, 34/1000, 24678/10000 )! What do you observe?

Now try with different numbers, like 2/5, 567/2,11/7, 78245/7, 2754/348. etc...

What do you oberve?

When finished click here to continue this little lesson!




1217. Before the introduction of the Arabic notation, multi-
plication was difficult, and the division even of integers called
into play the highest mathematical faculties. Probably nothing
in the modern world could have more astonished a Greek mathe-
matician than to learn that, under the influence of compulsory
education, the whole population of Western Europe, from the
highest to the lowest, could perform the operation of division
for the largest numbers. This fact would have seemed to him
a sheer impossibility. . . . Our modern power of easy reckoning
with decimal fractions is the most miraculous result of a perfect
notation. WHITEHEAD, A. N.

Introduction to Mathematics (New York,

1911), p. 59.

1614. The miraculous powers of modern calculation are
due to three inventions : the Arabic Notation, Decimal Fractions
and Logarithms. CAJORI, F.

History of Mathematics (New York, 1897),
p. 161.


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





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