Remember that we want to begin by assigning a variable to represent the repeating decimal.
See solution.
Practice makes perfect
We are asked how we can write a repeating decimal as a fraction. To write repeating decimals as fractions, we need to follow a few steps.
Step 1. Assign a variable to represent the repeating decimal.
Step 2. Write an equation to equate the variable and the decimal.
Step 3. Multiply each side of the equation by 10^d, where d is the number of repeating digits in the repeating decimal.
Step 4. Subtract equivalent expressions of the variable and the repeating decimal from each side of the equation.
Step 5. Solve for the variable. Write an equivalent fraction so that the numerator and denominator are integers, if necessary.
Let's take a look at an example. We will consider a repeating decimal 5.43 and assign variable x to it.
x = 5.43
Now we will multiply each side of the equation by 10^d, where d is the number of repeating digits in the repeating decimal. Since d=1 in our example, we will multiply both sides of our equation by 10.
10x = 54.3
Next, we will subtract equivalent expressions of the variable and the repeating decimal from each side of the equation. In our case, we will subtract x from the left-hand side and 5.43 from the right-hand side.
10x - x = 54.3 - 5.43
Let's solve this equation for x!
