Question

Turn 3.8 repeating into a fraction

Answer 1

To turn
`3.(8)=3.888...` into a fraction you shouls 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 3.(8), so you have x=3.888... .

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: 8. Now multiply both sides of the equation by
`10^1 = 10`. Thus, you have
`10x = 10 \cdot 3.888...` or
`10x = 38.888....`.

3 step. Subtract the equation in Step One from the equation in Step Two. Notice that when we subtract these equations, our repeating pattern drops off. Therefore,
`10x-x=38.888...-3.888...\\ 9x=35`.

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 = 35`. If you divide both sides by 9, you get
`x=(35)/(9)`. When simplified, you get that
`x=3(8)/(9)`.

Answer:
`3.(8)=3.888...=3(8)/(9)`.

Answer 2

The correct answer is 35/9, or 3 8/9.

Step-by-step explanation:
Let x=3.888.... This means that 10x=38.888....

Subtracting the two, we have
(10x=38.888...)-(x=3.888...), which gives us 9x=35.

Divide both sides by 9, and we get 35/9.