I'm confused, are these equal?
The problem says "the decimal 0.2511112222 (ending in 2s)" but the explanation says that that is "0.25 + 0.0011111.... + 0.0000001111...." Shouldn't that say "0.25 + 0.001111 + 0.0000002222......"? Also, they used 0.0000001111.... when solving the problem in the explanation.
@dashingrhinoceros Great question! Notice that the \(0.25\) is not repeating, it's just \(0.25\). But, the \(.0011111...\) and the \(0.00000011111...\) are both repeating. Add these two decimals together. From the 7th digit after the decimal point and onwards, you're adding \(1\) twice, so it accomplishes exactly what we needed! It's going to look like \(.0011112222...\) , which is the exact decimal we were looking for.
If you wanted to use \(.0000002222...\), you would need the \(.001111\) to not be repeating. That way, \(0.25\) + \(.001111\) + \(.0000002222...\) gives us the exact decimal. You can try out this version too on your own if you want, it should give you the same answer! I encourage you to give it a shot, it's always cool to get the same answer two different ways
Hope this helps!
@quacker88 Oh I understand now! Thank you!