In math there are many things that go hand in hand, for example addition and subtraction, also multiplication and division. Another thing that goes hand in hand is fractions and decimals. We can take a fraction and make it decimal but we can also have a decimal and make it into a fraction. In order to do so we need to understand the term “rational numbers”. Rational numbers are simply decimals that are terminating or repeating.
We can take the word “rational” we can take out the word “Ratio” meaning of integers (fraction of integers).
Terminating decimals are numbers like 0.55, 0.205, and 6.1 (these are all decimals that have a clear ending). We can make these decimal into fractions by paying attention to the place values that the digits hold. For example 0.55 is in the hundredths place therefore 0.55 is 55/100.
Repeating Decimal are numbers like 0.333333….., 0.77777….,and 0.242424 (decimals that have a repetition in the number. it may start later in the number). We can make these decimals in to numbers by setting them equal to “X”. A good example is 0.333333…. because we know of the top of our heads that it is 1/3 but do we know why it is? Below are the steps to show why 0.3333…. is 1/3.
Step 1) X=0.333333….
Step 2) 10X=3.333333…. (Find a number of ten that will get rid of the repeating end of the decimal. Then subtract Step 1 and Step 2.)
Step 3) 9X=3
Step 4) 9X/9=3/9 or 1/3
We can use these steps on any repeating decimals. Lets try the decimal 0.242424….! We will start the problem just like we did for 0.333……!
Step 1) X = 0.242424
Step 2) 100x = 24.2424 (We want to set it equal to 100X because it will move the decimal two places to the right and it will get rid of the repetition)
Step 3) 99X = 24
Step 4) 99X/99 = 24/99 or 8/33