Question

the number line shows point x. which number does point x represent on the number line? a 8.6 b 8.12 c 14.0 d 9.2

Explanation:

Step1: Determine the scale

Between 7 and 8, there are 5 small ticks. So each tick represents $\frac{8 - 7}{5}=0.2$.

Step2: Locate point X

From 8, we count the number of ticks to X. Let's see, from 8, moving right, how many ticks? Let's check the position. Wait, actually, let's re - evaluate. Wait, between 7 and 8, 5 intervals, so each interval is 0.2. Now, let's see the position of X. Let's count from 8. Let's see, 8 + (number of intervals from 8 to X)0.2. Wait, maybe another way: Let's see the distance from 7 to 8 is 1 unit, divided into 5 parts, so each part is 0.2. Now, let's see where X is. Let's count the ticks. From 7, each tick is 0.2. Let's count: 7, then 7.2, 7.4, 7.6, 7.8, 8, 8.2, 8.4, 8.6, 8.8, 9, 9.2... Wait, no, maybe I miscounted. Wait, the number line: 7, then some ticks, then 8, then more ticks, then X, then towards 11. Wait, maybe the scale between 8 and 9: let's see, from 8 to 9, how many ticks? Wait, maybe my first approach was wrong. Wait, let's look at the options. Option C is 14, which is way beyond 11, so eliminate C. Option B is 8.12, which is close to 8, but X is further from 8. Option A is 8.6, D is 9.2. Wait, let's re - examine the number line. Let's count the intervals. From 7 to 8: 5 intervals, so each interval is 0.2. From 8 to 9: also 5 intervals? Wait, no, maybe the number of intervals between 7 and 8 is 5, so each is 0.2. Then from 8, let's count the ticks to X. Let's see, X is after 8. Let's see, 8 + 60.2? Wait, no, maybe I made a mistake. Wait, let's check the options. Let's calculate the value for each option. Option D: 9.2. Let's see, from 8 to 9.2, the difference is 1.2, and since each interval is 0.2, the number of intervals is $\frac{1.2}{0.2}=6$. Let's see the number line: from 8, moving 6 intervals of 0.2 each: 8+60.2 = 8 + 1.2=9.2. Let's check the other options. Option A: 8.6, which is 8 + 30.2 = 8.6, but the position of X seems further from 8 than 3 intervals. Option B: 8.12, which is 8+0.12, but our interval is 0.2, so 8.12 is not a multiple of 0.2. Option C is 14, too big. So the correct answer should be D.

Answer:

D. 9.2