.3~

.3~ or .3 repeating is commonly thought to equal 1/3. Believers of this idea claim that because the number of decimals is infinite, that it must equal 1/3. They sometimes use the supporting example that .33333333=1/3, therefore .66666666=2/3 therefore .99999999= 3/3, or 1. To prove this wrong, you need to consider 2 things. First, and most sensible, 10 is not divisible by 3. Therefore, no matter how many .3's you use, they will never be able to complete the whole number 1. The second thing you need to consider is that with .33333~, you will always be off by just a little from achieving 1/3. This is why when you use a calculator and enter 1/3, the decimal given is .333333334.