- #1

dracobook

- 23

- 0

1/3 is equal to .333333...

2/3 is equal to 2*(1/3) or .66666...

3/3 is equal to 3*(1/3). If 1/3 is equal to .333... then wouldn't 3/3 be equal to .9999...? Also, isn't .9999... not the same as 1?

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- Thread starter dracobook
- Start date

- #1

dracobook

- 23

- 0

1/3 is equal to .333333...

2/3 is equal to 2*(1/3) or .66666...

3/3 is equal to 3*(1/3). If 1/3 is equal to .333... then wouldn't 3/3 be equal to .9999...? Also, isn't .9999... not the same as 1?

- #2

amcavoy

- 665

- 0

You should search this. Analogues of this question have come up before.

- #3

Hurkyl

Staff Emeritus

Science Advisor

Gold Member

- 14,967

- 19

Also, isn't .9999... not the same as 1?

Double negatives! I don't think you're asking quite what you meant to ask.

0.999~

Examples like the one you posted are demonstrations of why mathematicians decided to require that 0.999~ = 1 in the decimal number system: otherwise arithmetic would not work nicely.

- #4

HallsofIvy

Science Advisor

Homework Helper

- 43,021

- 970

Hurkyl said:Double negatives! I don't think you're asking quite what you meant to ask.

Actually, Hurkyl, reading the whole post I think this time the double negative was exactly what he meant. Many people who confuse the "decimal notation" for numbers with the numbers themselves think that 0.9999... is

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