User:MathMan64/CentigradeDegree
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[edit] Fractions
[edit] Repeating Decimals
A repeating decimal has digits in the decimal part that repeat forever, such as: 
A shortcut way of writing this is 
More examples:
or 
or 
Notice that the line is only over the part of the decimal that repeats.
[edit] Changing repeating decimals to fractions
[edit] If the entire decimal repeats
Change to a fraction.
This one has only one digit that repeats. So multiply by ten.
Then subtract the original number.
Subtract in two places: 
and 
[edit] Square root of a complex number
Each complex number has two square roots. Consider 
where 
and 
. The quadrant of 
is determined by the signs of a and b.
The square roots are 
where the signs match if 
, but are different, if not.
This can be derived by expressing 
So 
Equating the real and imaginary parts: 
and 
Solve the second equation for d: 
Substitute into the equation for the real part above to get 
Which simplifies to 
Solving this for 
gives 
So 
Solving for 
and doing similar work gives
