We will draw lines to connect each repeating decimal with an equivalent fraction. To do so we will find fraction form of each repeating decimal. Let's start with the first one.
To find the fraction form of 0.17 we will first represent the repeating decimal with the variable x. Then we will write an equation by setting this variable equal to 0.17.
x=0.17Since 0.17 has two repeating digits, we will multiply both sides of the equation by 10^2.
Next we will subtract x from both sides of the equation. Since x=0.17, we will substitute 0.17 for x on the right-hand side. Finally, we will solve the obtained equation for x.
We found that x is equal to 1799. Remember that x is also equal to 0.17. By the Transitive Property of Equality, we can conclude that the fraction is equal to the given repeating decimal number.
x= 0.17 x= 17/99 ⇒ 0.17= 17/99
With this information we can draw a line to connect the repeating decimal with the equivalent fraction.
We will follow the same steps to match the repeating decimals with their equivalent fraction forms.
Variable
Equation
Number of Repeating Digits (n)
Multiply Equation by 10^n
Subtract the Variable From the Equation
Solve for the Variable
Transitive Property of Equality
0.351
v
v= 0.351
3
v * 10^3=0.351 * 10^3
1000v=351.351
1000v-v=351.351-v
1000v-v=351.351- 0.351
999v=351
v&=351/999
&=13/37
0.351=13/37
0.17
w
w= 0.17
1
w * 10^1=0.17 * 10^1
10w=1.7
10w-w=1.7-w
10w-w=1.7- 0.17
9w=1.6
v&=1.6/9
&=16/90=8/45
0.17=8/45
0.351
y
y= 0.351
2
y * 10^2=0.351 * 10^2
100y=35.151
100y=35.151
100y-y=35.151- 0.351
99y=34.8
y&=34.8/99
&=348/990=58/165
0.351=58/165
0.351
z
z= 0.351
1
z * 10^1=0.351 * 10^1
10z=3.511
10z-z=3.511-z
10z-z=3.511- 0.351
9z=3.16
y&=3.16/9
&=316/900=79/225
0.351=79/225
Finally, we will draw the lines that connect the repeating decimals with their fraction forms.
