What is the rule in changing fraction to desimal?

Answer 1

The first rule is to spell decimal correctly, otherwise you might get an answer to something else!

There are three types of decimal numbers:

(a) terminating.

(b) recurring.

(c) neither terminating nor recurring.

The method, in each case is different.

TERMINATING

Count the number of digits after (to the right of) the decimal point. Call this number D.

The numerator of the fraction is the original decimal number written out without the decimal point. The denominator is 1 followed by D 0s. This fraction may need simplification.

Example:

23.456

There are 3 digit [456] after the decimal point so D = 3 and so the denominator is 1000.

So the fraction is 23456/1000 which can be simplified to 2932/125.

RECURRING

Count the number of digits in the string that repeats. Call this number R.

The numerator of the fraction is the original decimal number truncated (chopped off) after the first set of the repeating digits minus the original decimal number truncated before the repeating strings start. In both cases retain the decimal points. The denominator is the number formed by a string of R 9s ie 9, 99, 999 and so on. Again, the fraction may need simplification - it may first require multiplying numerator and denominator by a power of ten to get rid of the fractional part of the decimal.

Example:

17.35426426426....

The recurring string is 3 digits long [426] so R = 3 and so the denominator = 999

Numerator = 17354.26 - 17.35 = 17336.91

The fraction is 17336.91/999 = 1733691/99900 which simplifies to 577897/33300.

NEITHER

This is the decimal representation of an irrational number, not a rational number> Therefore, it cannot be expressed as a fraction. The best that you can do is to take the number formed by the first few digits and then treat it as a terminating decimal. This will give an approximate fraction.

Examples:

pi = 3.14159265359...

Let approx pi = 3.1416

Then following steps for a terminating fraction,

fraction = 31416/10000 = 3927/1250

If you had done approx pi = 3.14

then you would have had

fraction = 314/100 = 157/50.

Answer 2

The first rule is to spell decimal correctly, otherwise you might get an answer to something else!

Divide the numerator (top) of the fraction by its denominator (bottom), using long division. Keep going until the division comes to an end (remainder = 0) or until yu have enough decimal digits.