This might leave you feeling more than a little perplexed, but .99999 really does equal 1! TheCalculatorSite tells us how:
Proof 1:
If N = 0.999, then 10N = 9.99.
10N - N is therefore 9.99 - 0.999 therefore 9N = 9 therefore N =1
Proof 2:
If N = 0.999 then N divided by 9 is 0.111
Express this as the equation:
0.111 = 1/9
Multiplying both sides by 9 produces:
0.999 = 1
Luckily, they explain it all further:
What's going on here? In two words, 'decimal expansion'. 0.999 really represents 0.999999999 and on ad infinitum with each place to the right of the decimal point representing a further negative power of 10.
So the decimal expansion 0.9999... actually represents the sum 9/10 + 9/100 + 9/1000. Adding a further place of decimals (0.9999) would add just 9/10000 and so on into infinity until the two values are so close as to be indivisible.
