Answer:
0.222(repeating) = 2/9
Step-by-step explanation:
To convert a percentage to a decimal, divide by 100%.
22.2%(repeating)/100% = 0.222(repeating)
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To convert a repeating decimal to a fraction, first multiply it by 10 the the power that is equal to the number of repeating digits. Here, we have 1 repeating digit, so ...
x = 0.222(repeating)
10^1 · x = 10x = 2.222(repeating)
Now subtract the original. The repeating parts cancel.
10x -x = 2.222(repeating) - 0.222 repeating = 2
9x = 2
x = 2/9 . . . . . divide by the coefficient of x
The decimal is 0.222(repeating).
The fraction is 2/9.
