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Conversions between decimals and
fractions are straight forward.
To convert from a fraction to a
decimal, just carry out the division to the required number of
decimal points.
Examples:
In the last example the
decimal repeats, thus the bar above the repeating number 6; if we
limited the number of required decimal points, we would round the
last digit as necessary.
To convert the decimal back
to a fraction, write the decimal over the power of ten it names, then
reduce.
Examples:
In the first example, the
last decimal place is the hundredths place so we used 100 as the
denominator; likewise in the second example, 5 is in the thousandths
place so we used 1000 as the denominator.
Repeating decimals:
Many divisors will create
repeating decimals, and it's useful to be proficient recognizing
some of these repeating patterns. For example:
A more in depth (advanced)
handling of decimal to fraction conversions can be found here: Real
Numbers
Handling mixed numbers
requires that you keep the whole number part of the decimal number
separate from the fractional part. Converting a mixed fraction to a
decimal number simply requires division of the fraction to the number
of digits required, then adding the whole number. When converting a
decimal number greater than 1 to a mixed fraction, carry out the
procedure above with the fractional part of the decimal number and
place the result after the whole number part of the decimal number.
examples
