Repeating Decimals are decimal numbers that have number(s) after the decimal point that repeat in a pattern.

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1 5.5 Fractios ad Decimals Steps for Chagig a Fractio to a Decimal. Simplify the fractio, if possible. 2. Divide the umerator by the deomiator. d d Repeatig Decimals Repeatig Decimals are decimal umbers that have umber(s) after the decimal poit that repeat i a patter. We put a repeatig bar over the digits that repeat i a patter. (Make sure the bar oly goes over the digits that are repeatig.) EXs: Termiatig Decimals Termiatig Decimals are decimal umbers that ed. If you keep dividig, you will get a remaider of zero with o other digits i the divided to drop dow. They do ot have repeatig decimals ad the directios usually will ot tell you to roud your aswer. How to kow whe to stop dividig:. You have a remaider of zero with o other digits i the divided to drop dow. 2. If the directios tell you to roud your aswer, you will stop at oe place value after the give roudig place value.. You are able to recogize that the umber will have a repeatig decimal (ie. umbers behid the decimal poit that repeat i a costat patter).

2 Note: You ca tell whether a fractio will covert to a termiatig decimal by lookig at its deomiator. If the deomiator has a prime factorizatio cosistig of oly twos ad/or fives, the the decimal represetatio of the fractio will termiate (ed without roudig or havig a repeatig decimal). If the deomiator has a prime factorizatio cosistig of other factors tha 2 ad/or 5, the you will either eed to roud or have a repeatig decimal. Example : Chage 5 4 Solutio: Step : Simplify the fractio, if possible Step 2: Divide the umerator by the deomiator. d d Before we do the divisio we wat to look at what kid of decimal we should be edig with. Will it be a termiatig decimal or a repeatig decimal? (We already kow we do ot have to roud sice the directios do ot tell us to.) To see if we have a termiatig decimal we will look at the prime factorizatio of the deomiator, 6. If the deomiator has oly factors of 2 ad/or 5, the we kow we have a termiatig decimal Sice we oly have factors of 2, we kow we have a termiatig decimal. So, let s divide (Sice we kow we have a termiatig decimal, we will add zeros to the back of the divided util we get a remaider of zero.) You Try It : Chage Hece,

3 Example 2: Chage Solutio: Step : Simplify the fractio, if possible. is already simplified. Step 2: Before we divide, first let s look at the prime factorizatio of to see if we have a termiatig decimal Sice we oly have factors of 2 ad 5, we kow we have a termiatig decimal. So, let s divide.00 You Try It 2: Chage Hece, 0.5. But remember, we had. Therefore,.5. Example : Chage 2 Solutio: Step : Simplify the fractio, if possible. 2 is already simplified. Step 2: Divide the umerator by the deomiator. d d First, let s look at the prime factorizatio of 2 to see if we have a termiatig decimal Sice the prime factorizatio has more tha just 2 s or 5 s (it has a ), this will NOT be a termiatig decimal. Also, sice the directios did ot tell us to roud, we ca assume this will be a repeatig decimal. So, let s divide Hece, You ca see here that you will just keep gettig a 4 as a remaider. This meas the i the quotiet will just keep repeatig.

4 You Try It : Chage 5 2 Example 4: Chage 2 Solutio: Step : Simplify the fractio, if possible. 2 is already simplified. Step 2: Divide the umerator by the deomiator. d d First, let s look at the prime factorizatio of to see if we have a termiatig decimal. Sice the prime factorizatio has more tha just 2 s or 5 s (it has a ad ), this will NOT be a termiatig decimal. Also, sice the directios did ot tell us to roud, we ca assume this will be a repeatig decimal. So, let s divide Hece, You ca see here that the divisio is startig to repeat. You have (which is what you started with), the 0, ad the 00. So you kow that the 0. will repeat. You Try It 4: Chage 5 4

5 Simplifyig Expressios with Fractios ad Decimals To simplify expressios that cotai both fractios ad decimals, you eed to make the umbers look the same. This meas, you either eed to chage the fractios to decimals so that all your umbers are decimals. Or you eed to chage the decimals to fractios so that all your umbers are fractios. Example 5: Simplify..25 Solutio: Let s do this problem usig fractios. This meas we will eed to chage.25 ito a fractio So ow we have,. Let s get the LCD of ad simplify Hece, We ca also do the problem with decimals. This meas we will eed to chage i You ca use your calculator for this, 0.5 So ow we have, , agai, you may use your calculator to get, So, it is possible to get two differet aswers for this problem,.25 if you decide to work i fractio from, ad if you decide to work i decimal form. Either aswer is correct. You eed to pick which route you would like to take at the begiig (fractios or decimals) ad the you will oly eed to write oe as your aswer. Hece, your aswer is.25 OR You Try It 5: Simplify

6 Example 6: Simplify Solutio: Let s do this problem usig fractios. This meas we will eed to chage 0.5 ito a fractio So ow we have,. Let s get the LCD of 60 ad simplify Hece, You do NOT wat to do this particular problem usig decimals. The reaso beig is if you try to 2 chage ito a decimal you would get 0.6. You caot work with a repeatig decimal whe you are computig. You also caot roud sice the directios do ot tell you to do so. Therefore, you ca oly do this problem usig fractios. Ad therefore, there is oly oe possible correct aswer. 2 9 Hece, You Try It 6: Simplify