# can someone explain this math question?

ok so 1/3=.33 repeating so .33.......*3=.99........

1/3*3=1

.99 does not equal one

yes i know that 3/3=1

Relevance
• Philo
Lv 7

the infinite series 9/10 + 9/100 + 9/1000 ..... = 0.999.... does equal 1.

let S = 0.9999..........

then 10S = 9.99999..........

subtract the equations

9S = 9.00000........

S = 1

• pyz01
Lv 7

OK

1/3 = .333 and the 3 repeats forever. So to show this truly accurately you need to either show the 3's repeating on and on or you could decide to stop the 3 (let's after three places and show this:

1/3 = .333 1/3

Now when you multiply 1/3 x3 = 1

.333 1/3 x 3 = .999 + 0001/3 3 times or .001

= 1

So you see, as stated above, .999999 repeating does really equal 1 or, because the 3 repeats forever, at some point, it approaches 1 when it is added to other repeating 3s.

Hope this helps.

To say that mathematicians have "proved" 0.99.... = 1 gives the impression that it was ever an open question.

It's important to realize that 0.99... is a symbol which refers to a number.

People are so used to seeing decimals represent numbers which are not whole, and are so committed to the fallacious idea that every number has only one decimal symbol representation.

.9999 repeating represents 1 in our Mathematical system; which is just a system that we, as humans, developed to help explain the world around us, this is only base 10 mathematics. There is so much we do not know. Mathematics makes assumption; We do this because it is necessary to explain the world around us. It is just another "language."

Source(s): I'm a professional nerd. Oh, and All American Mathlete 1984

Mathematicians have proved that 0.999999 repeating is equal to 1, try a google search to find the proofs.

You answered it yourself. The math doesn't lie. For example:

1/9 = 0.1111.....

Let's have x = 0.1111.... = 1/9

x * 9 = 1 because 1/9 * 9 = 1

Therefore 0.1111.... * 9 must = 1

Therefore 0.9999.... = 1