Yes, 0.9999999.... repeating to infinity equals 1 sharp (not approximately).
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9 repeating = infinity. If you mean 0.9999... repeating as a fraction, that is equal to 1. Proof: 1/3 = 0.3 repeating (0.3333...) 2/3 = 0.6 repeating (0.6666...) 1/3 + 2/3 = 3/3 = 1 0.3333... + 0.6666... = 0.9999... 0.9999... = 1 End of Proof:
0.3... repeating or 33.33.... repeating %
0.9 recurring is equal to 1. While this seems illogical, this can be proven by saying that, if 0.3 recurring is equal to 1/3, then 1/3 x 3 = 0.9 recurring, or 1.
1.3333 repeating
To show that a decimal number is of a repeating nature, simply insert a horizontal bar over the numerals that are repeating. When typing, you may also underline the repeating digits or place them in parentheses.A few examples:1/3 = 0.33333333 = 0.(3)1/6 = 0.16666666 = 0.1(6)1/11 = 0.09090909 = 0.(09)1/24 = 0.04166666 = 0.041(6)