Does 0.999... Equal 1?

[steven787]

Menago KF said:
Generally it does.

Put it this way: 0.9999.....does not equal 1, BUT

0.(9) is equal one. So one someone aska you what 1/3 is in numbers you give the answer 0.(3) . Multiply 0.(3) by three and that is equal to 1/3 times 3. And that equals one.

If someone doesn't get what i'm saying, when you write some number like 0.9999999........... ==> that does not mean that the number is infinate. It ends at some distant point that you can't accurately pinpoint, but it still ends.

In this case the () with a number inside means that the number goes on for infinity.

And because 0.(9) goes on for infinity, it is so close to the actual 1 that it is percieved to be that number.

 

Thank you.  But I don't like the wording of the last sentence. Perception may matter when measuring a circle for a drawing or building.  But when working sets of data, a lot of precision is lost.

1/3+1/3+1/3 = 1 and .(3) + .(3) + .(3) = .(9) no big deal.

but when you have 1/3 + 2/7 + 6/11 + 4/13 + 9/17 + 3/23 = .... that would lose a lot of accuracy if you convert each component to a decimal before adding them up.