How do you change a decimal fraction to an equivalent fraction?

Answer 1

In theory there are three types of decimal fractions: terminating, recurring and non-recurring infinite.

For a terminating fraction, count the numbers of digits after the decimal point and call that number d. Then write a fraction with numerator equal to the decimal fraction but without the decimal point and the denominators equal to 1 followed by d zeros. That ratio is an equivalent fraction though it may be possible to simplify it.

For example:

Given 98.765, d = 3 (the digits 765)

So equivalent fraction = 98765/1000

For a recurring decimal, count the number of digits from the decimal point to the point before the recurring pattern begins, d and count the number of digits in the recurring pattern, r. Then, build the fraction as follows:

Numerator = the number formed to d+r digits after the decimal point minus the number formed to ddigits after the decimal point.

Denominator = r 9s followed by d 0s.

For example,

12.789656565.... recurring

d = 3

r = 2

So Numerator = 5 digits after the decimal point - 3 digits after the dp

= 1278956 - 12789 = 1266167

and denominator = 2 nines followed by 3 zeros = 99000

So equivalent fraction = 1266167/99000.

Finally, you cannot be given an infinite, non-recurring decimal fraction. It will have to be approximated.