Each decimal number can be written as a fraction where the denominator is some power of 10.
D
Start by using a variable to represent the given repeating decimal number. Then, write an equation by setting the variable and the decimal equal to each other.
A
7/10
B
7/9
C
3/20
D
5/33
Practice makes perfect
Remember that we can write any decimal number as a fraction where the denominator is some power of 10. With this in mind, let's write 0.7 as a fraction.
0.7=7/10
We want to write the given repeating decimal number as a fraction.
0.7
To do so, we will follow five steps.
Assign a variable to represent the repeating decimal.
Write an equation by setting the variable and the decimal equal to each other.
Multiply both sides of the equation by 10 to some power, where the power is the number of repeating digits in the repeating decimal.
Solve for the variable. Let's do it! First, we are going to use the variable N to represent the given repeating decimal number. This can be written as an equation.
N=0.7
Since the given number has one repeating digit, we will multiply both sides of the equation by 10^1=10.
We want to write 0.15 as a fraction. Recall that we can write any decimal as a fraction where the denominator is some power of 10.
0.15=15/100
Notice that we can reduce the fraction we got. Let's do it!
Let's consider the given repeating decimal.
0.15
We can write this decimal as a fraction the same way we did in Part A. Again, we will use the variable N to represent the given decimal number. This can be written as an equation.
N=0.15
Since the given number has two repeating digits, we will multiply both sides of the equation by 10^2=100.
