Question 338279
<font face="Garamond" size="+2">


Divide 7 by 18 on your calculator. You get 0.38888888888888888888888888888889, which really means that it is 0.38 followed by repeated 8s forever.  Since writing that many digits is not only impractical but impossible, we have a shorthand notation.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{7}{18}\ \approx\ 0.38888888888888888888888888888889]


is only approximate (very, very close, but still approximate)


But if you say


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{7}{18}\ =\ 0.3\overline{8}]


which means zero point three followed by an infinity of eights, we now have a manageable and exact representation.


If you have a decimal fraction that has a group of digits that repeat, you run the line over the entire group that repeats.  For example:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{7}\ \approx\ 0.142857142857142857]


but we can write:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{1}{7}\ =\ 0.\overline{142857}]


Again, notice the assertion of exactness.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
My calculator said it, I believe it, that settles it
<img src="http://www.evolvefish.com/fish/media/E-FlyingSpaghettiEmblem.gif">
</font>