fractions to reccuring decimal

fractions to reccuring decimal

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Could you be a little more specific? Two thirds for example can't be expressed exactly as a decimal with a finite number of figures, but a calculator will work out 0.6666etc easily enough. Is it an idea you are exploring?
ianmoth
26 November 2011
Let us take a random reccuring decimal like 0.343434....
mrtmaths
27 November 2011
Start by letting it be equal to x. If we now multiply it by 100, 100x becomes equal to 34.343434... Now we have a simple simultaneous equation, x= 0.343434... and 100x = 34.343434.. We can now subtract one equation from the other, say 100x - x = 34.3434...-0.3434... which gives 99x = 34
mrtmaths
27 November 2011
We now know what is equal to 99x so if we divide both sides of this equation by 99 we have the solution x = 34/99 and so we can cofidently say that 0.343434... = 34/99, but do not take my word for this, check the answer on your calculator. Anymore clarification needed please do not hesitate to contact me.
mrtmaths
27 November 2011
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