i dont knw how to write the decimals as comon fractoins in simplest form? - XP Math - Forums

 XP Math - Forums i dont knw how to write the decimals as comon fractoins in simplest form?

 09-15-2010 #1 coolj999     Join Date: Sep 2010 Posts: 3 i dont knw how to write the decimals as comon fractoins in simplest form? :conf used::icon_c rying::icon _crying:
09-16-2010   #2
MAS1

Join Date: Dec 2008
Posts: 249

Quote:
 Originally Posted by coolj999 :conf used::icon_c rying::icon _crying:
Here are a couple of examples for terminating decimals:

1. 0.465
Look at a non-zero digit which is in the smallest place. In this case it is the 5 in the thousandths place. This means the denominator for your fraction will be 1000. Now write the digits "465" in the numerator. You should have:
465/1000 which is four hundred sixty five thousandths.
Now see if you can simplify the fraction. 5 is a factor of both the numerator and denominator so divide both by 5 giving
93/200

2. 2.76
Ignore the whole number part for now.
0.76 = 76/100 = 38/50 = 19/25
Now add the whole number part back in creating the mixed number 2 19/25

To find the fraction for non-terminating, repeating decimals:

1. 0.33333...
Let x = 3.33333...
then 10x = 3.33333...
10x - x = 3.3333... - 0.3333...
9x = 3 (All of the 3's to the right of the decimal place cancel out)
x = 3/9 = 1/3

2. 0.166666...
Let x = 0.166666...
10x = 1.66666...
10x - x = 1.66666... - 0.1666666...
9x = 1.5
18x = 3
x = 3/18 = 1/6

3. 0.142857142857142857...
x = 0.142857142857142857...
1000000x = 142857.142857142857142857...
1000000x - x = 142857
999999x = 142857
x = 142857/999999 = 15873/111111 = 5291/37037 = 1/7

Hope this helps!

 09-17-2010 #3 Mr. Hui     Join Date: Mar 2005 Posts: 10,609 I wonder what happens when you try to simplify 0.999... ? __________________ Do Math and you can do Anything!
 09-22-2010 #4 meetballs     Join Date: Mar 2010 Posts: 46 1/7 is the Answer
10-23-2010   #5
MAS1

Join Date: Dec 2008
Posts: 249

Quote:
 Originally Posted by meetballs 1/7 is the Answer
Ummm, no.

12-03-2010   #6
Lisasmith111

Join Date: Nov 2010
Posts: 36

Quote:
 Originally Posted by Mr. Hui I wonder what happens when you try to simplify 0.999... ?
Mr Hui,
I guess using the above method we would have

x= 0.9999; 10x = 9.9999

so 10x - x = 9.9999 - 0.9999

then 9x = 9

so x = 1

0.9999... is as near to 1 as makes no odds

What do you think?

Lisa Smith

 12-04-2010 #7 Mr. Hui     Join Date: Mar 2005 Posts: 10,609 Thanks for typing it out, Lisa. The fact that 0.999... is so close to 1, and the difference between 0.999... and 1 is infinitesimally small, "proves" that 0.999... = 1. __________________ Do Math and you can do Anything!
12-06-2010   #8
tiger190

Join Date: Oct 2010
Posts: 8
yup

Quote:
 Originally Posted by Mr. Hui Thanks for typing it out, Lisa. The fact that 0.999... is so close to 1, and the difference between 0.999... and 1 is infinitesimally small, "proves" that 0.999... = 1.
i agree wit u

12-20-2010   #9
Lisasmith111

Join Date: Nov 2010
Posts: 36

Quote:
 Originally Posted by Mr. Hui I wonder what happens when you try to simplify 0.999... ?
Mr Hui,

I think this one becomes 1 as the following illustrates:-

let x = 0.999 and 10x = 9.999

10x - x = 9
9x = 9
x = 1

0.999 is approx = 1 (I guess there has to be some rounding at due to the nature of decimals, whereas fractions can be more exact.

12-24-2010   #10
MAS1

Join Date: Dec 2008
Posts: 249

Quote:
 Originally Posted by Lisasmith111 Mr Hui, I think this one becomes 1 as the following illustrates:- let x = 0.999 and 10x = 9.999 10x - x = 9 9x = 9 x = 1 0.999 is approx = 1 (I guess there has to be some rounding at due to the nature of decimals, whereas fractions can be more exact.
Lisa, there is no rounding involved. 0.999999999... is exactly equal to 1 by the reasoning you showed. If x = 0.99999999... and 10x = 9.999999... then when you subtract x from 10x, it cancels out all of the 9's to the right of the decimal point.
10 - x = 9.999999... - 0.99999999...
9x = 9
x = 1
Substituting back gives 1 = 0.99999...

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