Let n = 0.0123456789 recurring 1010n = 123456789.0123456789 recurring 1010n - n = 123456789 9999999999n = 123456789 n = 123456789/9999999999 = 0.0123456789 recurring Therefore the recurring decimal 0.0123456789 expressed as a fraction is 123456789/9999999999. Check it out on your calculator.
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To indicate a decimal recurring to infinity , we write 0.262626... (Note three sets of terms and three or more dots/full stops) To convert to a fraction Let P = 0.262626.... Then 100 P = 26.262626.... Subtract. 99P = 26 ( Note the recurring decimals subtract to zero. ) Hence 99P = 26 P = 26/99 This fraction will NOT reduce any further. Hence 0.262626.... = 26/99
Oh, dude, you're hitting me with some math here. So, if we're breaking down 0.269 with just the 2 and 9 recurring, that's like saying it's 269 repeating over 990. It's like trying to catch a never-ending train ride with only two carriages. Enjoy the ride, man.
BRO ITS A DECIMAL POINT
The fraction 5/7 as a decimal is a recurring decimal, represented as 0.714285... The bar notation is used to indicate the repeating pattern, which in this case is 714285. Therefore, the decimal form of 5/7 is 0.714285 with the digits 714285 repeating indefinitely.
7/9 as a fraction becomes 0.777... as a decimal . It repeast to infinity. NB The three dots/stops/periods at the end of the decimal, indicate to mathematicians that it is a decimal repeating to infinity.