caudovittatus

Hi I've decided to go back to the books and refresh my maths knowledge... I'm going over the introductory section of Engineering Mathematics by K. A. Stroud. In the section on unending decimals he gives examples of how to convert an unending decimal into a fraction which goes like so (I haven't used his exact words below): To convert 0.18181818 recurring into a fraction you multiply [math]0.\dot{1}\dot{8}[/math] by 100 So: [math] 100 \times 0.\dot{1}\dot{8} = 18.\dot{1}\dot{8} [/math] Then if you subtract [math]0.\dot{1}\dot{8}[/math] from both sides you get: [math] 100 \times 0.\dot{1}\dot{8} - 0.\dot{1}\dot{8} = 18.\dot{1}\dot{8} - 0.\dot{1}\dot{8} = 18 [/math] That's fine so far, but he goes on (as printed in the Fifth edition): " That is: [math] 99 \times 0.\dot{1}\dot{8} = 18.0 [/math] This means that: [math] 0.\dot{1}\dot{8} = \frac{18}{99} = \frac{2}{11} [/math] My problem is with [math]99 \times 0.\dot{1}\dot{8} = 18.0[/math] because I would have expected that to be [math]99 \times 0.\dot{1}\dot{8} \approx 18.0[/math] or am I just being dense? If you can explain why it is equal I'd greatly appreciate it. Thanks in advance!