Is it true that 0.999.... = 1?
The explanation follows from simple arithmetic. We know that the fraction "one third" can be written as "0.333...." (the "..." means that the string of numbers goes on forever). So we have 0.333.... = 1/3. Multiply both sides by 3: 0.999... = 1. This is a proposition in pure numbers and it does not involve any approximation, nor any units of measurement. Mathematics is always interesting: mathematics with an infinite number of digits is particularly interesting because you can find truths that are surprising.
More Info:
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What are your thoughts on this subject?
270 Comments
Alan Richter
Stupid question. Does $999 dollars equal $1,000. Nooooo!!
123
May 26, 2016 10:07PM
David Grover
No, 1=1. Rounding a number up does not change the actual value of that number.
85
May 27, 2016 9:43PM
Nina Kamwene
I concur, .999 is rounded off to 1 in my daily life, but it not actually 1.
67
May 26, 2016 10:29PM
Dave Mackey
They could string out 9's forever,and it would still not equal 1.
44
May 27, 2016 9:51PM
Daniel Parker
This one is wrong. 1 is 1. 0.999 is 0.999. It is as simple as that.
33
May 28, 2016 10:55PM
Wilma Tomlinson Mcphail
Your answer is WRONG!!
27
May 30, 2016 1:02AM
Donald WH Andrews
I thought these questions were rated before they could come on here.
26
May 28, 2016 1:32AM
Bill Coe
Please report this BS question using the button on the top right. I try to get questions published with limited success and something like this gets through the review process???
20
Dec 23, 2016 6:01AM
Mike Bourey
Wrong! Just like the soap that claims to be 99.9 percent pure still has a .1 percent of impurities.
Somebody took a nibble out of THAT enchilada!!
16
Dec 23, 2016 12:56AM
Alan Richter
Bewley Steve it does not say if a cent. .999 of a cent cannot exist. It in simply comparing 2 numbers that can never be equal without rounding.
14
Jan 13, 2017 3:08PM
Atul Kalra
WRONG. It is an approximation.
0
Apr 15, 2024 3:37PM
Owen Tucker
Great question… Answer is short and concise yet could have gone on splain that numbers are simply a human construct.
0
Jan 25, 2024 3:35AM
David Carney
Approximation was not in the clue. Your new math is wrong
0
Oct 18, 2023 1:02AM
Wendy Wilkins Valdez
Decimals cannot accurately depict 1/3 because of the approximation of the fraction. Adding .333333333333 three times will NEVER equal 1 because of that approximated decimal. Fractions themselves, on the other hand, can add together to equal a whole. So, this is an outright disaster of a question.
0
Jul 13, 2023 9:50PM
Player
In the case of an infinite decimal, again standing in for the kind of infinite sequence of terminating decimals we saw above, we identify the sequence with its limit. This is what we mean when we say that 0.999... = 1
0
May 27, 2023 9:58AM
Patty K
Rounded up, yes, but does it actually and totally equal 1? No, it will always be a little short
2
Apr 22, 2023 10:30AM
Leslie Hayden
This is very badly worded. "is .99999 equal 1" is a yes or no answer not true or false. Should be worded ".9999.. = 1" true or false. Of course that totally ignores the fact that while .99999... approaches 1, it is never equals the value.
2
Apr 20, 2023 5:29PM
Kath Thomson
David Grover, read the explanation again. IN MATHS 0.999...= 1 and it has nothing to do with rounding a number up.
0
Apr 17, 2023 5:21PM
Kath Thomson
Alan Richter, different situation entirely. IN MATHS 0.999....=1. Read the explanation again. Even maths would not say that 999=1000 - it doesn't.
0
Apr 17, 2023 5:18PM
therandolph
.99999999999999999999 will never be equal to 1. This answer is wrong
3
Mar 19, 2023 5:37PM
Helga U. Williams
A little bit of kids' stuff here?
🙄
0
Feb 28, 2023 7:34PM
George Brungot
Alan Richter, Not the same. the three periods after the .999 mean that the 9's repeat forever.
0
Feb 2, 2023 6:14PM
Richard Rubright
Is it true.... takes an answer of the form [yes,no], not [true,false].
1
Jan 21, 2023 10:23PM
JayJay
This is WRONG. Who came up with this ridiculour question and incorrect answer pair? 👎
4
Jan 16, 2023 8:18AM
Steve Edwards
All those saying the answer is incorrect obviously don’t just not understand mathematics but also haven’t read the explanation in the answer that gives a good proof that 0.999…. (recurring forever) DOES exactly equal 1. Although it seems as if this is not possible, and that it should be a small amount less than 1, the question in this case would have to be “tell me how much less than 1, 0.999… actually is?” Because it’s impossible to say what the difference between the two numbers is, they must be the same.
The proof that these are the same is a fairly standard and easy proof that children at the age of 15 learn in Secondary school in the U.K. and I’m sure around the world too.
3
Jan 1, 2023 9:14PM
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