The farther the number of diopters is from 0, the greater power of the corrective lens.
Most Nearsighted: Patient 7 Most Farsighted: Patient 3 Best Eyesight: Patient 2
Practice makes perfect
The corrective powers of contact lenses for eight people are shown on the given diagram. Let's start by looking at our diagram!
We know that the farther the number of diopters is from 0, the greater power of the lens. We also know that positive diopters correct farsightedness and negative diopters correct nearsightedness. We want to find who is the most nearsighted, who is the most farsighted, and who has the best eyesight. Let's do these things one at a time.
Most Nearsighted
To find who is the most nearsighted, we will find the patient whose contact lenses have the negative corrective power farthest from 0 diopters. Let's start by selecting all patients who have negative power in their contact lenses.
We can see that Patient 1, Patient 4, Patient 5, Patient 6, and Patient 7 are nearsighted. Now, let's plot the powers of their contact lenses on a number line.
The power of - 7.5 diopters is farther from 0 diopters than - 4.75, - 3.75, - 2.5, and - 1.25 diopters, so the power of Patient 7's lenses is the farthest from 0. This means that Patient 7 is the most nearsighted.
Most Farsighted
To find who is the most farsighted, we will find the patient whose contact lenses have the positive corrective power farthest from 0 diopters. We can start by selecting all patients who have positive power in their contact lenses.
We can see in the diagram that Patient 2, Patient 3, and Patient 8 are farsighted. Now we will plot the powers of their contact lenses on the number line. Let's do it!
Our number line shows that the power of 2.5 diopters is farther from 0 diopters than 1.5 and 0.75 diopters. This means that the
power of Patient 3's lenses is the farthest from 0, so Patient 3 is the most farsighted.
Best Eyesight
To find the patient with the best eyesight, we will find the patient with the power of lenses closest to 0 diopters. Recall that the absolute value of a number is its distance from 0 on the number line. The absolute value of a non-negative number is equal to the number, while the absolute value of a negative number is equal to its opposite.
We can calculate the absolute value of all powers to find the distance between each power and 0 diopters. Let's do it!
Patient
Power (diopters)
Distance from 0 Diopters
1
- 1.25
|- 1.25|=1.25
2
0.75
|0.75|= 0.75
3
2.5
|2.5|= 2.5
4
- 3.75
|- 3.75|=3.75
5
- 2.5
|- 2.5|=2.5
6
- 4.75
|- 4.75|= 4.75
7
- 7.5
|- 7.5|= 7.5
8
1.5
|1.5|= 1.5
Next, we can plot the distances on a number line to see the order from least to greatest.
We can see on the number line that the number that is the farthest to the left is | 0.75|. This means that the power of Patient 2's lenses is closest to to 0 diopters. Patient 2 has the best eyesight.
