If 0.9999999… goes on infinitely adding nines after the decimal, will it equal 1? Yes. It catches people’s temporal senses off-guard, but Dr. Math shows us the mathematics and reasoning behind this. Infinity is 1 although it may seem that you are always a speck short. But infinity of 9’s lingers as long as One does. The Math Forum shows the proof that this is the case, but an easy way to think about it is the conversion of fractions:
2/3 = 0.666…
1/3 = 0.333…
2/3 + 1/3 = 3/3 = 1
0.666… + 0.333… = 0.999…
1 = 0.999…
2 comments
hank says:
Oct 23, 2006
2/3 is not 0.666….. it is 0.666…….7 hence 2/3 + 1/3 = 1!
liquid parallax says:
Oct 24, 2006
I don’t know where you got that from hank. Your calculator rounds up for decimal place limitation, but actually dividing 3 by 2 by hand (long division shown below) will yield a repeating 6 after the decimal point infinitely.
0.66
3 / 2.000
18 |
20
18 |
20
… sorry if that doesn’t look like a division problem. Anyway, you subtract 18 from 20 and will always end up with a 2, then carry the zero and you are back to square one and add 6 after 6 after 6 after 6 after (you get the picture)…