Using a double number line, the length of Antonio's key chain is 35 millimeters.
To find the answer, we can start by labeling one line in centimeters and the other line in millimeters. Then, we can plot the given measurements and use the ratio of 50 millimeters to 5 centimeters to find the length of Antonio's key chain in millimeters.
Here's how the double number line would look:
0 1 2 3 3.5 (key chain) 4 5
|--------|--------|--------|--------|-----------------------|--------|
0 10 20 30 40 50 60 70 80
We can see that 5 centimeters is equivalent to 50 millimeters, so we can mark both of those on the double number line:
1 centimeter = 10 millimeters
5 centimeters = 50 millimeters
3.5 centimeters = 35 millimeters
0 1 2 3 3.5 (key chain) 4 5
|--------|--------|--------|--------|-----------------------|--------|
0 10 20 30 40 50 60 70 80
50
|
5
Next, we can plot the length of Antonio's library card, which is 80 millimeters:
0 1 2 3 3.5 (key chain) 4 5
|--------|--------|--------|--------|-----------------------|--------|
0 10 20 30 40 50 60 70 80
50
|
5
|
80
Finally, we can use the ratio of 50 millimeters to 5 centimeters to find the length of Antonio's key chain in millimeters. Since his key chain is 3.5 centimeters long, we can mark that on the double number line and then draw a line connecting it to the millimeter scale:
0 1 2 3 3.5 (key chain) 4 5
|--------|--------|--------|--------|-----------------------|--------|
0 10 20 30 40 50 60 70 80
50
|
5
|
80
Thus, we can conclude that the length of Antonio's key chain is 35 millimeters.