### Instruction: Write $0.\overline{43}$ as a simplified fraction.### Response: To convert a repeating decimal to a fraction, I need to use a trick to eliminate the repeating part.
Let me call the decimal x, so x = 0.\overline{43}.
If I multiply both sides by 100, I get 100x = 43.\overline{43}.
Notice that the decimal part on the right is the same as x, so I can subtract x from both sides.
This gives me 99x = 43.\overline{43} - 0.\overline{43} = 43.
Solving for x, I get x = 43/99.
This is already in lowest terms, so I'm done.