Question

Which rational number equals 0 point 4 with bar over 4?

Answer 1

Answer: 4/9

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Work Shown:

`x = 0.\overline{4}\\\\x = 0.4444\ldots\\\\10x = 4.4444\ldots\\\\10x-x = 4.4444\ldots-0.4444\ldots\\\\9x = 4\\\\x = (4)/(9)\\\\(4)/(9) = 0.\overline{4}= 0.4444\ldots\\\\`

The idea is that when we subtract 10x and x, the infinite decimal pattern (the 4s that go on forever) will cancel. That leads to 9x = 4 which solves to x = 4/9