Common sense argument as to why 0.9999... = 1

If you want to run a distance of 1 meter then you must first run 90% of the distance, and then 90% of the remaining distance, and then 90% of the remaining distance again, ad infinitum.

i.e. the distance in meters you must run is 0.9 + 0.09 + 0.009 + ...
which sums to 0.999...

So unless the sum adds up to 1 it's impossible to run 1m, which is nonsense.

Hence 0.999... = 1.

If you want to run a distance of 1 meter then you must first run 80% of the distance, and then 80% of the remaining distance, and then 80% of the remaining distance again, ad infinitum.

i.e. the distance in meters you must run is 0.8 + 0.08 + 0.008 + ...
which sums to 0.888...

So unless the sum adds up to 1 it's impossible to run 1m, which is nonsense.

Hence 0.888... = 1.