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Decimal to Fraction

To transform a decimal to fraction you must look at the number in the way which I quickly show you (if this is what you want).

NOTE: However, there exist another path which can open a wider insight into converting fractions.



Look at what comes before and after the point (or comma)

then look how many digits there are after (to the right of) the point (or comma): the number of digits tells you the decimal places involved (e.g. tenth, hundreth, thousandth, etc...), that is the place value of your decimals is the denominator of your fraction.

then you simplify the result by reducing fractions to their lowest terms.


0.45 = 45 hundreths, so 0.45=45/100


2,368 = 2 and 368 thousandths, that is 2 and 368/1000

that is 2 + 368/1000 which is turn is also equal to 2000/1000 + 368/1000 = 2368/1000

Again, this can be simplified by dividing both term by 8 (the Greatest Common Factor or GCF).

So the final result is 2.368 = 296/125



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601. The first thing to be attended to in reading any algebraic
treatise is the gaining a perfect understanding of the different
processes there exhibited, and of their connection with one an-
other. This cannot be attained by the mere reading of the book,
however great the attention which may be given. It is impos-
sible in a mathematical work to fill up every process in the man-
ner in which it must be filled up in the mind of the student before
he can be said to have completely mastered it. Many results
must be given of which the details are suppressed, such are the
additions, multiplications, extractions of square roots, etc., with
which the investigations abound. These must not be taken on
trust by the student, but must be worked out by his own pen,
which must never be out of his own hand while engaged in any
mathematical process. DE MORGAN, A.

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



Related pages

Adding fractions.

Fractions to decimals

Decimal to fraction

A nice presentation of the method on this external website














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