diffy said:
maze said:
arildno said:
arildno said:
arildno said:
This is true, but be fair to the young'uns. This is far beyond high school mathematics. It is even beyond the typical Calc 1/2/3/... sequence required of all science and engineering undergraduates in most colleges. Science majors do study advanced math, but it is stuff like Green's theorem, complex analysis, numerical methods, ... That [tex]0.\bar{9}=1[/tex] is even beyond a lot of high school math teachers. I know, because long, long ago I saw the simple 9*0.111... "proof" and pointed it out to a high school math teacher who insisted I was wrong. I didn't learn that I was right until I went to college and took a real algebra course. Bottom line: We should go a bit easy on the kind of people who typically ask this question.LukeD said:
D H said:
Yes, .9 recurring (or .999...) is equivalent to the decimal representation of the number 1. This can be proven mathematically through various methods, such as using infinite geometric series or converting to fractions.
This concept can be difficult to grasp, but it essentially comes down to the fact that the decimal system has limitations in accurately representing certain numbers. Just like how 1/3 in decimal form is represented as .333..., 1 in decimal form is represented as .999...
No, .9 recurring is not an approximation of 1. It is the exact representation of 1 in the decimal system. It may seem like an approximation because our minds have been conditioned to think of numbers with finite decimal representations, but mathematically, it is equivalent to 1.
Sure, one example is the concept of repeating decimals in the metric system. For instance, 1 meter is equivalent to 1.000... meters, but we typically round it to 1 meter for simplicity. This is similar to how .9 recurring is equivalent to 1, but we often round it to 1 for ease of understanding.
The concept of .9 recurring equaling 1 may seem trivial, but it has significant implications in fields such as calculus and number theory. It also challenges our understanding of numbers and the limitations of the decimal system. Additionally, it serves as a reminder to always question and critically think about mathematical concepts.