Follow-Ups to Answer from Expert Victor S. Miller

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the teach wrote at 2006-09-12 06:54:47
In simple terms, as I am an 8th grade math teacher and have to find simplest ways to explain things.



Set up simultaneous equations, lets use the decimal 0.123123123...



So 1 equation is x= 0.123123....



Now make an equation with the same x, putting 1 whole repeating sequence before the decimal.



So 1000x = 123.123123....



It became 1000x because we moved the decimal over 3 spaces to put one "123" before the decimal

(since multiply by 1,000 you just move the decimal over 3 spaces)



now subtract 1 equation from the other



1000x = 123.123123....

-   x =   0.123123....

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999x = 123    (notice the decimals cancel out)



so x = 123/999 which reduces to 41/333

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