N = 2.045045045...

On the right, move the decimal just to the right of the end of the first cycle
of repeating digits, multiply the left side by the power of 10 corresponding to
the moving of the decimal on the right.

In other words, multiply both sides by 1000

1000N = 2045.045045045...

Subtract the original equation

1000N = 2045.045045045...
    N =    2.045045945...
-------------------------
 999N = 2043
    N = 2043/999
    N = 227/111

Edwin


 

Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!
 
Since you posted this in the Sequences-and-series section, maybe you wanted to
see it done as an infinite geometric series:

2 + .045
  + .000045
  + .000000045
  + ...........

2 + 0.045 + 0.000045 + 0.000000045 + ...

2 + 4.5x10-2 + 4.5x10-5 + 4.5x10-8 + ...

The terms to the right of 2 form an infinite geometric series with first term =
a1 = 4.5x10-2 and common ratio r = 10-3





Multiply numerator and denominator by 103





So the fraction is  or 

Edwin
 

RELATED QUESTIONS

Express the following repeating decimal as a fraction in the lowest term.

______... (answered by neatmath)

express 0.7(repeating decimals ) as a... (answered by stanbon)

Write the repeating decimal 0.7575 . . . as a... (answered by jim_thompson5910,richwmiller)

Write the repeating decimal 3.15555555 as a... (answered by MathLover1)

Write the repeating decimal as a fraction:... (answered by rfer)

How to write the repeating decimal .9999..... as a... (answered by Fombitz)

write each repeating decimal as a fraction in simplest form:
1. 0.5 repeating 
2. 0.4... (answered by Alan3354)

How do you express 2.135 repeating, the 35 is repeating, as a... (answered by richard1234)

Could you help me express this repeating decimal as a fraction?... (answered by stanbon)