Confusing math trick!!!?

Question

How is this true.
1/3=.333... correct?
2/3=.666... correct?
3/3=1? or should it be .999...?
1/3(.333)+2/3(.666)=3/3( .999 or 1)?
It cannot equal .999 because everybody knows any number divided by itself = 1. But, .333 +.666 equals .999, Could somebody explain how this is possible? Thank you

Answer 1

.9999 for infinitely many digits is the same thing as 1.
.333...+.666...=1

Answer 2

The answer to the equations are not that simple

1/3=0.333 333 333 333 333 333 333 333 333 333 33
2/3=0.666 666 666 666 666 666 666 666 666 666 67 3/3=1

The "7" is the factor that allows the 3/3=1 to be posible
You where tricked by your teacher i bet.
The equation is right but the results as you posted in your questions are wrong.
You need a calculator that can display allot of numbers to understand.

Here's a REAL math trick:
111,111,111 X 111,111,111 = ?

Try it.

Answer 3

when you say .333 or .666, that is out of 1000.

To accurately represent 1/3 is to not divide it at all. Same with 2/3, do not divide it. Technically 1/3 gives an infinite of 3's after the decimal.

Answer 4

I agree with all these people. they said it better than I ever could.
.333 and .666 are infinite, therefore it does not equal .999, but 1.

Answer 5

I think you answered your own question - math trick!

1/3 is represented by the decimal .333...to infinity.
It is therefore an approximation anytime it is used - whether you add, subtract, divide or multiply with it. As an approximation, your answer will be an approximation - and .9999....to infinity is certainly approximately equal to 1.

Note: I don't buy into .999.....to infinity as being equal to 1, although I'm sure some of your answers will indicate this.

Answer 6

Ah! The very essence of computational error! A computer can only hold a finite number of digits and must approximate in many instances. A computer or calculator would consider 1/3 to be equal to 0.33333333 to as many digits as it can hold in memory.

A calculator or computer would consider 2/3 to be equal to 0.66666666667 rounding the last digit to 7 (if it has a smart error-reducing algorithm) or 0.66666666666 if not. In both cases this would only go to as many digits as the machinr can hold in memory.

The reality is that neither 0.333333, nor 0.666666 nor 0.66667 are accurate. These are close approximations to 1/3 and 2/3, but not exactly the same and there is some error or discrepancy in the answers.

That's why they don't add up to 1 on the calculator, but they do in real life.

Answer 7

You stopped at too few decimal places.
.333 + .666 = .999,
but .333... + .666.... does not = .999.
Eventually to make this work, you must round, and then you will discover that
.3333333 + .6666667 = 1.000000...

Answer 8

Unfortunately in the world of Mathematics everything does not end up in whole numbers. There is such a thing as "Repeating Decimals" which will repeat a decimal out to infinity.

In practical applications, 1.333 would be the same as 1/3, But: 1.336 would be 1.34 The 6 would be dropped and the second 3 would be change upward to a 4.
Three significant figures are used in Engineering.

I have included a website for you that will explain more about repeating decimals. If the URL is hidden please run your cursor over the bottom of this example.
http://search.yahoo.com/bin/search?p=REPEATING%20DECIMALS

Answer 9

1/3 and 2/3, like so many other fractions, produce what is called a repeating decimal. That is, the decimal number (in our case, .333333333333333 and .666666666666, etc) go on for ever without bound or stop.

To divide anything by itself will yield one.

3/3 = 1

one/one = one

1/2 over 1/2 = 1

apple/apple = 1

I hope this helps.
Guido

Answer 10

1/3 doesn't equal .333. It's close but not spot on. you can't divide 10 by 3, it's an imperfect number.