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mathematical problem ..
This question is right, just as the teacher said in class.

In fact, 0.999999999 (there are infinitely many 9s) and 1 are completely equal!

Before proving, we must first understand a mathematical law.

0.99999999999 ... and 0.999...999 are two completely different numbers in mathematics. The former means that the number of 9 is infinite; The latter means that the number of 9 is limited, so it is generally necessary to indicate the number of 9 after it.

Therefore, 0.999999999 ... means that the number of 9 is infinite, which must be clear first. Then we can use the knowledge of geometric series to prove the above conclusion. The proof process is as follows:

0.999999999 ...= 0.9+0.09+0.009+0.0009+...= 0.9 *( 1-0. 1N)/( 1-0. 1)

Therefore, 0.99999999 = 1 is effective.