User:MathMan64/CentigradeDegree
Fractions
[edit]Repeating Decimals
[edit]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.
Changing repeating decimals to fractions
[edit]If the entire decimal repeats
[edit]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
Square root of a complex number
[edit]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