Why Is 1 = .9999999? Answers in Math & Logic Forums

  • Thread starter honestrosewater
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In summary, there is a discussion about whether or not to post a sticky in the math or logic forum about the 1=.99999999... concept. Some suggest having a sticky in all general forums including an FAQ, while others believe it's important to continue helping those who don't understand the concept. Warren proposes having an FAQ post written by mentors in order to provide an introduction and quick explanations for common topics in the "general" subforums. Rachel adds that it's just a thought and open for discussion.
  • #1
honestrosewater
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Why doesn't someone post a sticky in the math or logic forum about the 1=.99999999... thing?
Or for that matter, a sticky in all the general forums including FAQ?
 
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  • #2
While these incessant threads are pretty annoying, it's not really right of us to just shut down any discussion of the topic. There will always be a constant stream of people who do not understand this bit of math, and we have an obligation to continue to help them -- not just provide a sticky and tell them to go away.

- Warren
 
  • #3
:approve:
What I had in mind was a more of an FAQ post; something the mentors could write up and refer people to as an introduction. Of course, if someone still had questions after reading the FAQ post, they should be free to ask.
There are other topics which come up regularly and can quickly be explained. The "general" subforums seem like good places for such FAQ posts.
Just a thought
Rachel
 
Last edited:

1. Why is 1 equal to .9999999?

The reason for this is due to the concept of rounding in mathematics. While 1 and .9999999 may appear to be different numbers, they are actually equal when rounded to a certain number of decimal places. In this case, both numbers would be rounded to 1 when rounded to the nearest whole number, making them equal.

2. Can you prove that 1 equals .9999999?

Yes, there are multiple ways to prove this mathematically. One way is to use the concept of limits in calculus, which shows that as the number of decimal places increases, the difference between 1 and .9999999 approaches zero. This means that they are essentially the same number.

3. How can a number be equal to a repeating decimal?

While it may seem counterintuitive, repeating decimals can represent a finite number. In the case of .9999999, the number is equivalent to 9 repeating infinitely. This means that the number is just slightly smaller than 1, but when rounded, it becomes 1.

4. Is .9999999 considered a rational or irrational number?

.9999999 is considered a rational number because it can be written as a fraction, in this case 9/9 or 1. Rational numbers are numbers that can be expressed as a ratio of two integers, while irrational numbers cannot be written as a fraction.

5. Why is this concept important in mathematics?

The concept of .9999999 being equal to 1 is important in mathematics because it challenges our understanding of numbers and their representations. It also highlights the importance of precision and rounding in mathematical calculations. Additionally, understanding this concept is essential for more advanced mathematical concepts such as limits and infinite series.

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