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You can put this solution on YOUR website!
\n" ); document.write( "Here is a variation of the process shown by tutor @alan3354.
\n" ); document.write( "(1) n = 0.233333...
\n" ); document.write( "(2) 10n = 2.33333...
\n" ); document.write( "Subtract (1) from (2):
\n" ); document.write( "9n = 2.1
\n" ); document.write( "n = 2.1/9 = 21/90 = 7/30
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\n" ); document.write( "Here is a different method, without using algebra.
\n" ); document.write( "0.2333333... = 2.333333.../10 = (2 1/3)/10 = (7/3)/10 = 7/30.
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\n" ); document.write( "And here is a shortcut that is based on the basic algebraic method.
\n" ); document.write( "The numerator of the fraction is (a) all the digits up through the first cycle of the repeating digits, minus (b) just the non-repeating digits. In this example, that is 23-2 = 21.
\n" ); document.write( "The denominator of the fraction is one 9 for each repeating digit, followed by one 0 for each non-repeating digit. In this example, with one non-repeating digit and one repeating digit, that is 90.
\n" ); document.write( "The fraction is then 21/90 = 7/30.
\n" ); document.write( "That shortcut is a great time saver if speed is important, as in a math competition. Here are a couple of further examples of this method.
\n" ); document.write( "2 non-repeating digits; one repeating:
\n" ); document.write( "0.4166666... = (416-41)/900 = 375/900 ( = 5/12)
\n" ); document.write( "3 repeating digits, 2 non-repeating:
\n" ); document.write( "0.12345345345... = (12345-12)/99900 = 12333/99900 (which can also be simplified, if required) \n" ); document.write( "