+150 0.9=9/10.
I think can be like this:
\(0.999...=\frac{9}{10}+\frac{9}{100}+\frac{9}{1000}+...\)
\(0.999...=\frac{9}{10}+(\frac{9}{10})(\frac{1}{10})+(\frac{9}{10})(\frac{1}{10})^2+...\)
Using infinite geometric series, with a=\(\frac{9}{10}\) and r=\(\frac{1}{10}\):
\(0.999...=\frac{\frac{9}{10}}{(1-\frac{1}{10})}=\frac{9}{10}\times\frac{10}{9}=1\)
Hope this help.
+180 Nice Answer James!
But, I would like to think of it a different way.
0.9 cannot be equal to 1 only \(0.\overline{9}\) can. If you are meaning\(0.\overline{9}\) then, I can show you how to do it.
1/9 = \(0.\overline{1}\)
2/9 = \(0.\overline{2}\)
3/9 = 1/3 = \(0.\overline{3}\)
And so on this means that when we come to 9/9 = \(0.\overline{9}\)=1
🐺🐺🐺
