# Proof that 495 = 499.5!

1. Jul 10, 2010

### zeromodz

Sorry, I typed the wrong thing in the title, I meant 495.5 = 495

(1/3) + (1/3) + (1/3) = 1
(0.333333333333) + (0.33333333333) + (0.33333333333) = 1
0.999999999999999 = 1
99.9999999 = 100 (Multiplied by 10)
99.1 = 99 (Subtracted 0.9)
495.5= 495 (Multiplied by 5) <---------------PROOF

2. Jul 10, 2010

### pbandjay

Operations on infinite decimal representations need to be considered more carefully.

3. Jul 10, 2010

### Office_Shredder

Staff Emeritus
This is not how subtraction is done

100-.9=99?

99.9999999... -.9=99.1?

Both wrong. Even if we assume that you flipped the equation so 100-.9=99.1, 99.99999-.9 is not 99

4. Jul 10, 2010

### Werg22

The second one is right.

5. Jul 11, 2010

### Mentallic

Umm... both 100-.9=99 and 99.999...-.9=99.1 are wrong. So I don't know what you're on about, plus it would've been a lot easier for the reader to determine which "second one" you're talking about by quoting just the relevant equality, not the entire post.

6. Jul 11, 2010

### disregardthat

No, 99.9999...-0.9 = 99.0999... = 99.1 is correct.

7. Jul 11, 2010

### uart

There was nothing wrong with what Werg said. Yes $(99.9999... - 0.9)$ really is equal to 99.1.

I cant believe this senseless OP is going to come back to yet another $0.9999... \neq 1$ debate.

8. Jul 11, 2010

### Mentallic

Oh yes of course, I didn't even stop to think about it once I saw all the recurring decimal places were cut off.