### Instruction: Express $0.6\overline{333}$ as a common fraction.### Response: To express a repeating decimal as a common fraction, I need to find a way to eliminate the repeating part by subtracting two equations.
I can start by letting x be the value of the repeating decimal, so x = 0.6\overline{333}.
Then, I can multiply both sides by 10 to shift the decimal point one place to the right, so 10x = 6.\overline{333}.
Next, I can multiply both sides by 1000 to shift the decimal point three more places to the right, so 10000x = 6333.\overline{333}.
Now, I have two equations with the same repeating part on the right, so I can subtract the first one from the second one to eliminate it.
This gives me 10000x - 10x = 6333.\overline{333} - 6.\overline{333}.
Simplifying, I get 9990x = 6327, which is a non-repeating decimal.
To solve for x, I can divide both sides by 9990, so x = 6327/9990.
This is the common fraction that represents the repeating decimal.