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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: 7,664

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)

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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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