Question

What is 8.3 repeating as a fraction?

Answer 1

For this case we have the following decimal:
 8.3
 To find the fraction equivalent expression, what we must do is multiply the decimal by 10 and divide the result by 10.
 We have then:
 $8.3* \frac{10}{10}$
 Rewriting we have:
 $\frac{83}{10}$
 Answer:
 The decimal written as a fraction is given by:
 $\frac{83}{10}$

Answer 2

To turn $8.(3)=8.333...$ into a fraction you should do such steps:

1 step. Set up an equation by representing the repeating decimal with a variable. Using your example, you will let x represent the repeating decimal 8.(3), so you have x=8.333... .

2 step. Identify how many digits are in the repeating pattern, or n digits. Multiply both sides of the equation from Step 1 by $10^n$ to create a new equation. Again, using your example, you see that the repeating pattern consists of just one digit: 3. Now multiply both sides of the equation by $10^1 = 10$. Thus, you have $10x = 10 \cdot 8.333...$ or $10x = 83.333....$.

3 step. Subtract the equation in Step 1 from the equation in Step 2. Notice that when we subtract these equations, our repeating pattern drops off. Therefore, $10x-x=83.333...-8.333...\\ 9x=75$.

4 step. You now have an equation that you can solve for x and simplify as much as possible, using x as a fraction: $9x = 75$. If you divide both sides by 9, you get $x=\dfrac{75}{9}$. When simplified, you get that $x=\dfrac{25}{3}$.

Answer: $8.(3)=8.333...=\dfrac{25}{3}=8\dfrac{1}{3}$.