Converting

[Magmaman101]

I am in ninth grade next year, I didn't really pay attention last few years or retain what I learned because I didn't want to... So I plan to catch up this summer to the point I should be at in math.. I already learned adding/subtracting/multiplying/dividing fractions again really fast, (I basically absorbed it )so, but I am stuck on converting to decimals and back to fractions, its like my brain just does not understand it, or I can't get my brain to understand it... so does anyone have a clear explanation of how to do it?

 

[stapel]

I am stuck on converting to decimals and back to fractions....

does anyone have a clear explanation of how to do it?

Loads of people have great explanations! But which explanation suits your taste is up to you. So start looking at some of the lessons available online, and find some that make sense to you.

Have fun!

 

[Otis]

Converting from fractions to decimals requires long division (which you already absorbed). Are you more interested in converting from decimals to fractions?

Some of those are easy to do mentally, like 0.75 converts to 75/100 (by inspection) and reduces to 3/4.

Others are more involved; please provide an example for which you are stuck. :cool:

 

[Bob Brown MSEE]

Algorithm

Here's a way to calculate the fraction
1) Multiply by a number that moves the decimal to the beginning of the repeating digits.
Remember the number for step 6.
2) Drop all the digits to right of decimal, just past the first repetition.
3) Replace the decimal point with a plus sign, leaving the sum of two integers.
4) Divide the second integer (right of + sign) by a number like 9, 99, or 999.
The number of 9's in the divisor should equal the number of digits above it.
5) Combine the sum into a fraction.
6) Divide by number remembered from step 1.
7) Reduce fraction to lowest terms.

Example: 1.3461538461538...
1) times 10 = 13.461538461538...
2) 13.461538
3) 13+461538
4) 13+461538/999999
5) 175/13
6) 175/13/10 = 175/130
7) 35/26

Example: 0.5833333333333...
1) times 100 = 58.33333333333...
2) 58.3
3) 58+3
4) 58+3/9
5) 175/3
6) 175/3/100 = 175/300
7) 7/12

Example: 6.02020202....
1) times 1 = 6.02020202....
2) 6.02
3) 6 + 02
4) 6 + 02/99
5) 596/99
6) 596/99/1 = 596/99
7) 596/99

 

[Bob Brown MSEE]

By Proof

Example: 1.3461538461538...
1) times 10 = 13.461538461538...
2) 13.461538
3) 13+461538
4) 13+461538/999999
5) 175/13
6) 175/13/10 = 175/130
7) 35/26

Let x be the answer that we seek,
I will number the proof steps and provide reasons
1:          x =      [COLOR=#333333]1.3461538461538...  [/COLOR]// given
2:        10x =       [COLOR=#333333]13.461538461538...[/COLOR] // times 10
3: 10000000 x = [COLOR=#333333]13461538.461538[/COLOR][COLOR=#333333]461538...[/COLOR] // times 10000000
4:  9999990 x = [COLOR=#333333]13461525                 [/COLOR]// 10000000x - 10x
5:          x = [COLOR=#333333]13461525[/COLOR]/9999990         // divide 9999990
6:          x =  35/26                   // factor 384615