February 4th
February 4th
Decimals and their Equivalent Fractions
Question: What is the equivalent fraction for
the decimal 4.422?
Misconception
The common misconception here is that decimals and
fractions are different typesof numbers.
Hence there is no equivalent fraction for this or any
other decimal.
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Correct
You can express the decimal as 4 and (the fraction)  . These are fraction equivalents.
These can be simplified by dividing both numerator and
denominator by 2 to give
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Further Explanation
The method above shows how to obtain an equivalent fraction
from a decimal. It is even easier to find the decimal equivalent
of a fraction. All you have to do is to use division.
So, for example, the decimal equivalent of the fraction  is 0.25 as 1.00 divided by 4 will give this result.
Similarly the fraction  can be expressed as a decimal by dividing 3 by 5 to
obtain 0.6
A similar way of achieving this is to find an equivalent
fraction that has either 10 or 100 or 1000 etc. as the
denominator. In this way we can determine the fraction equivalent
from the resulting numerator. For example,
and so the decimal equivalent is 0.6.
Similarly for more complicated fractions such as  . We can find its decimal equivalent by multiplying
both numerator and denominator by 25. This gives
and so the decimal equivalent is 0.075
If you are still feeling confused about equivalent decimals
and fractions, then think of a number line in which all numbers
are represented. A small part of such a number line is shown
below with numbers shown as decimals above the line and fractions
below the line
You can readily see, for example, that 
Note: What happens when the fraction cannot
be expressed as an equivalent fraction with a numerator of 10 or
100 or 1000 etc.?
An example of this is the fraction  . You can though divide 1.0000000......... by 3 to
give 0.33333.......... This is called a recurring decimal, and is
often denoted by putting a dot on top of the number (or numbers)
that repeat. So we can write
There are many other fractions that give rise to recurring
decimals, often with a group of digits that repeat. For example
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