# How in the world do you simplify repeating

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decimals when changing them to fractions. I'm helping my DS with this and just can't explain it to where he gets it. Thanks,

Here's an example of a problem:

.1333..... we get how to change it to a fraction just not doing a great job on simplifying it.

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Because 0.13333 has a single repeating digit (3), multiply the repeating decimal by 10 (if you had 0.464646, then you have two repeating digits (46) and you would multiply by 100, etc.). Then subtract the two numbers:

10 x 0.13333 = 1.33333

1 X 0.13333 = 0.13333

9 x 0.13333 = 1.2

Dividing both sides by 9:

0.13333 = 1.2/9

Multiplying top and bottom by 10 to get rid of the decimal,

0.13333 = 12/90

Simplifying, 0.13333 = 2/15.

I hope this formats correctly AND is helpful!

Oops: I see you already got the fraction and you need help simplifying the fraction? 12/90: dividing both top and bottom by 6 gives the 2/15

Martha

Edited by Martha in GA
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decimals when changing them to fractions. I'm helping my DS with this and just can't explain it to where he gets it. Thanks,

Here's an example of a problem:

.1333..... we get how to change it to a fraction just not doing a great job on simplifying it.

For solution see: How to represent a recurring decimal number as a rational number.

Best regards.

MPCtutor

http://www.mpclasses.com/ContactUS.htm

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AP Calculus, AP Physics, IIT JEE Test Prep.

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US Central Time:1:28 PM 9/17/2010

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To give an example from Saxon Algebra II, here's the system they use:

.01623232323 (in other words with the bar over the 23)

To convert it to a fraction:

In the number above, we will refer to .1623 as N

Take 100N = 1.623

Subtract N = .01623

Difference: 99N = 1.607

N = 1.607 / 99

Multiply numerator and denominator by 1000

N = 1607 / 99,000

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In the case of three repeating numbers such as 1.031543543543

(543 are the repeating numbers)

the same is done, but the number is multiplied by 1000

1000N = 1003.1543

Minus N = 1.0031

999N = 10002.1512

divide both sides of the equation by 999

N = 1002.1512 / 999

Multiply numerator and denominator by 10,000

N = 10,021,512 / 9,990,000

HTH

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Honestly, if you get *how* to turn it from a repeating decimal into a fraction, you are doing better than 98% of the free world. I'd accept unsimplified forms of those fractions, particularly for crazy ones like Teachin' Mine's example of N = 10,021,512 / 9,990,000 which could certainly be simplified by dividing by 2 or 4 or maybe even 8 (LOL), but goodness, it's enough that the kid got the problem IMHO.

LoriM (who has to look up that procedure EVERY YEAR I teach it! LOL!)

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Wow! Thanks for this nifty bit of information!

Blessings,

April

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