Exercise 10 Page 11

Tomas wanted to learn 15 students' opinions about whether summer break should be longer. He calculated the division of the number of students who said yes by the total number of students. The result is given as follows. 0.9333... We will write the number as a fraction. To do so, we will follow five steps.

1. Assign a variable to represent the repeating decimal.
2. Write an equation by setting the variable and the decimal equal to each other.
3. Multiply both sides of the equation by 10^d, where d is the number of repeating digits in the repeating decimal.
4. Subtract equivalent expressions of the variable and the repeating decimal from each side of the equation.
5. Solve for the variable. If necessary, write an equivalent fraction so that the numerator and denominator are integers.

Let's do it!

Steps 1 and 2

We will use the variable x to represent the given repeating decimal number. We can write an equation by setting this variable equal to 0.9333.... x=0.9333...

Step 3

Note that the given number has one repeating digit, so we will multiply both sides of the equation by 10^1.

Step 4

From here we will subtract x from both sides of the equation. Since x=0.9333..., we will substitute 0.9333... for x on the right-hand side.

Step 5

Next, we will solve the obtained equation for x. We found that x is equal to 1415. Remember that x is also equal to 0.9333... By the Transitive Property of Equality, we can conclude that the fraction is equal to the given number. x= 0.9333... x= 14/15 ⇒ 0.9333...= 14/15 Therefore, 0.9333... is equal to 1415.