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summarize the two methods for expressing fractions as decimals.decribe when it is appropriate to ise each method in your summary

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Converting Fractions and Decimals
 
Fractions to Decimals
 
I'm sure you are familiar with every day conversions of fractions to decimals such as:
 

¼ = 0.25 or having one quarter of something such a dollar. (1 quarter = 25 cents)

½ = 0.5 or having half a pizza pie or 50 cents out of a dollar

¾ = 0.75 or having 3 quarters of the pizza pie or 75 cents out of a dollar 

 
You can turn a fraction into a decimal 2 ways:
 
1. Divide the numerator by the denominator
 
 
2 or "2 fifths" can be converted by dividing the top      
5                     number by the bottom number. 
 
2 ÷ 5 = 0.4  
 
 
 
 
 
 
 
The Second Method: Rename the fraction so that the denominator is a power of 10 (i.e., 10 or 100 or 1000)
 
 
Method 2:
 
3 = 3x2  =  =  0.6
5    5x2     10 
 
 
convert 11
             40    
need to take bottom number and multiply it by some number until you get 10, 100, 1000, etc.
                     
40 x 25 = 1000
 
so now multiply both the top number and the bottom by 25
 
11  =  11  x 25  =  275    =  0.275   that's your answer  
40       40 x 25  =  1000
 
 
I hope this helps a little. Good Luck
                       
 
 
 
Consider 7/12=ai/10 +  a2/102 +a3/103 +... where all the aj are integers 0,1,2,3,4,5,6,7,8,9
Multiply  by 10 to get
             70/12 =5+10/12 = a1 +  a2/10 +a3/102 +...  which gives that a1=5 and
10/12 = a2/10 +a3/102 +a4/103+... 
Multiply  by 10 to get
100/12 =8 + 4/12= a2 +a3/10 +a4/102+... which gives that a2=8 and
4/12 = a3/10+ a4/100+...
Multiply  by 10 to get
40/12 =3 + 4/12= a3+ a4/10 +a5/102+...which gives that a3=3 and same remainder as before
its all 3's
 
If you do the same problem by long division, the appearance is different but the procedure is almost the same
 
12|7. 0 0 0 0                     12 into 70 = 5
     6 0
     1 0 0                            12 into 100 = 8
        9 6
           4 0                          12 into 40 = 3
           3 6
             4                           same remainder as last time
This gives the same sequence of remainders as last time.  The adding zero is the same as multiplying by 10
I DEARLY WISH THAT THERE WAS A CLEAR WAY TO EXPRESS LONG DIVISION USING THIS SYSTEM
 
Use which ever method is more comfortable.  There really is no "appropriate" in the question.
 
 
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
 
 
 
 
 
Please see:
 
In summary:
Convert Fractions to Decimals
1. The simplest method is to use a calculator. Just divide the top of the fraction by the bottom, and read off the answer !

Example: What is 5/8 as a decimal ... ?

... get your calculator and type in "5 / 8 ="

The answer should be 0.625

2. To convert a Fraction to a Decimal manually, follow these steps:

Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.
Step 2: Multiply both top and bottom by that number.
Step 3. Then write down just the top number, putting the decimal point in the correct spot (one space from the right hand side for every zero in the bottom number)
 
I hope this helps.
 
Jim G.

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