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**Byhalk****Guest**

Work out a fraction that is equivalent to 0.2*428571*

The star signs resemble a reacuring parts. pleeease help me i would apprieciate

**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,626

Quick way:

It has a similar pattern to 1/7, which is 0.1428571428571...

So I tried 0.2428571 x 7 = 1.7

And so the fraction would be 17/70

(Or 1.7/7, but it isn't right to mix decimals in fractions, so multiplying top and bottom by 10 fixes it)

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**kylekatarn****Member**- Registered: 2005-07-24
- Posts: 445

Byhalk wrote:

Work out a fraction that is equivalent to 0.2*428571*

The star signs resemble a reacuring parts. pleeease help me i would apprieciate

First of all, a recurring digit is written like this

x.(y)

but you cant represent with a fraction "numbers" that have two infinite periods (2 recurring parts) - 0.2(2)428571(1)

if the '2' repeats until infinity....there's no 'normal' mathematical way of representing [....]42857111111111111111111111111(1).... after that with a fraction.. Unless you invent a new kind of math ; )

Normal infinite periodic decimals are easy to convert into fractions.

0.(A) = A/9

0.(AA) = AA/99

0.(AAA) = AAA/999

.

.

.

0.(A.......A) = (AAA.......A)/(9*9*9*.......*9)

examples:

0.22222222222222222222... = 0.(2) = 2/9

0.45454545454545454545... = 0.(45) = 45/99

0.12312312312312312312... = 0.(123) = 123/999

0.552212355221235522123... = 0.(5522123) = 5522123/9999999

5.33333333333333333333... = 5.(3) = 5+ 0.(3) = 5+3/9

and so on...

*Last edited by kylekatarn (2005-09-22 10:08:50)*

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

My way is to turn the decimal into one recurring decimal and one terminating one. Taking yours as an example:

0.2*428571* = 0.*142857* + 0.1 = 142857/999999 + 1/10 = 1428570/9999990 + 999999/9999990 = 2428569/9999990 = 17/70.

I realise that was already said, but this shows how to get the solution to any problem.

Why did the vector cross the road?

It wanted to be normal.

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