let me add to the other answers:

make sure the fraction is in simplest form

look at the denominator

write the denominator as a product of prime factors

if you see only 2's, only 5's or a combination of 2's and 5's only, then the decimal equivalent will be a terminating decimal

if you see any other prime numbers other than 2's and 5's, then the decimal equivalent will be a repeating decimal

if the decimal equivalent is terminating you can use one of two methods, either divide the denominator into the numerator and divide until the division process stops or
*terminates*, thus the term terminating decimal;

or, write the fraction as an equivalent fraction whose denominator is a power of ten(10, 100, 1000, 10,000, etc) and then write the decimal

if the decimal equivalent is repeating, you use only one method-divide the denominator into the numerator and divide until you clearly see what repeats

let's look at some fractions whose decimal equivalents are repeating:

2/3=0.666... (the denominator is 3, *not* 2 or 5)

5/7=0.714285714285714285714285...(notice the denominator 7 and notice that the repetend is six digits in length-714285; so it is important that you divide enough times so that you clearly see what repeats !)

8/9=8/(3x3)

8/9=0.888...

4/11=0.363636... (the denominator is 11, *not* a 2 or a 5)

just to be sure, the denominator is on the outside of the symbol and the numerator is inside the symbol when you divide;add zeroes one at a time until you are finished

7/12=7/(2x2x3)

7/12=0.58333... (the 3 in the factorization makes the decimal repeat; the 2's give the decimal what is called a lag; the lag is what preceeds the repetend-the lag is 58)

15/22=15/(2x11)

15/22=0.6818181... (the 11 causes the decimal to repeat and the 2 gives the decimal the lag which is 6)

there is a way to determine how many digits there will be in the repetend and a way to determine how many digits will be in the lag; if you want to learn this let me know

let's look at some fractions whose decimal equivalents are terminating; here you can either divide until the division terminates or you can use equal fractions

3/4=3/(2x2)

each 2 needs a 5 and each 5 needs a 2 to make a power of ten

multiply 3 by 5x5 and multiply (2x2) by 5x5 to get 75/100=0.75

17/20=17/(2x2x5)

multiply the numerator and the denominator by 5(one 2 has a 5 but the other 2 does not !!)

(17x5)/(20x5)=85/100=0.85

9/16=9/(2x2x2x2)

multiply the numerator and the denominator by 5x5x5x5 (there are *4* 2's and none of them have a 5)

(9x5x5x5x5)/(2x2x2x2)(5x5x5x5)=5625/10,000=0.5625

3/40=3/(2x2x2x5)

multiply the 3 and the 40 both by 5x5(there are 3 2's but only 1 5)(the number of 2's and the numbers of 5's must be equal)

(3x5x5)/(2x2x2x5)x(5x5)=75/1000=0.075(the 5 goes in the thousandths place and the 7 goes in the hundredths place, therefore you put a 0 in the tenths place)

47/125=47/(5x5x5)

47x(2x2x2)/125x(2x2x2)=376/1000=0.376

you can make up your own examples for practice