Question 37339
<pre><font size = 3><b>If an infinite decimal such as .999... is to represent one specific number,
it should be the limit of the sequence described by part (a), in this case 1;
that is, .999...= 1. A number is a *limit* if the difference between it and the
terms of the approximating sequence is eventually less than any distance you
choose, no matter how small. What number does .4999...represent? 
<font color = "blue">
.4999··· = .4 + .0999··· = .4 + .1(.999···) = .4 + .1(1) = .4 + .1 = .5 
</font>
What about 7.562999...? Why? 
<font color = "blue">
7.562999··· = 7.562 + .000999··· = 7.562 + .001(.999···) = 7.562 + .001(1) =
7.562 + .001 = 7.563

Edwin McCravy
AnlytcPhil@aol.com</pre></font>