How do you express a decimal as a fraction in simplest form?

Answer 1

Make the decimal a fraction, which is usually one or two digits over 100. Decimal percentages will be expressed using larger denominators.

One way of saying this is to write the numbers after the decimal, over 1 followed by as many 0's as there are numbers after the decimal.

Examples:

.5 = 5/10

.28 = 28/100

.402 = 402/1000

.5525 = 5525/10000

Reduce the fraction to its simplest form by dividing the numerator and denominator by the same number, which is the same as dividing by 1.

Example:

28/100 divided by 4/4 = 7/25 -- this is the simplest form

402/1000 divided by 2/2 = 201/500 -- this is simplest form (201 = 67x3)

5525/10000 divided by 25/25 = 221/400 -- this is simplest form (221 = 13x17)

the numbers after the decimal over 1 followed by as many 0's as there are numbers after the decimal.
1) You convert the decimal to a fraction.

2) You simplify the fraction in the usual way.

For step 1, count the number of decimal digits. Use a "1", followed by that many zeros, in the denominator. Write the decimal number WITHOUT a decimal point in the numerator. Here is an example: Convert 3.225 to a fraction. Three decimal digits; so the denominator is 1000 (three zeros); your fraction is 3225 / 1000.

For step 2, the prime factors of the denominator can only be 2 and 5; for example, you don't need to check whether both numbers are multiples of 3, or of 7 - they won't.