Rewrite as a simplified fraction.

Question

\[\large{3.\overline{2} = {?}}\]

Answer 1

To simplify the decimal 3.\overline{2} as a fraction, we can assume that there is a repeating block of 2 after the decimal point.

To represent the repeating decimal as a fraction, we'll assign a variable to the decimal:
Let x = 3.\overline{2}

Next, we'll remove the repeating part by multiplying the entire equation by 10 (to get rid of the decimal):
10x = 32.\overline{2}

Now, we'll subtract the original equation from the new equation to eliminate the repeating part:
10x - x = 32.\overline{2} - 3.\overline{2}
9x = 29

Finally, we divide both sides of the equation by 9 to solve for x:
x = 29/9

Therefore, the simplified fraction of 3.\overline{2} is 29/9.