Question

which point on the number line shows 0.4?
0.0 a b 0.5 c d 1.0
point a point b point c point d

Explanation:

Step1: Determine the interval length

From 0.0 to 0.5, there are 4 intervals (since between 0.0, then the next mark, then A, then another mark, then B, then to 0.5). Wait, actually, let's count the number of segments between 0.0 and 0.5. From 0.0 to 0.5, how many equal parts? Let's see the marks: 0.0, then a mark, then A, then a mark, then B, then a mark, then 0.5. Wait, no, let's calculate the length of each interval. From 0.0 to 1.0, there are, let's see, from 0.0 to 0.5 is half, and from 0.5 to 1.0 is half. Wait, between 0.0 and 0.5, how many intervals? Let's look at the points: 0.0, then first mark, A, second mark, B, third mark, 0.5. So from 0.0 to 0.5, there are 4 intervals? Wait, no, the distance from 0.0 to 0.5 is 0.5, and if we count the number of spaces between 0.0 and 0.5: from 0.0 to first mark: 1 space, first to A: 1, A to second:1, second to B:1, B to third:1, third to 0.5:1? Wait, maybe better to calculate the value of each interval. Let's see, from 0.0 to 1.0, the number line is divided. Wait, 0.0, then a mark, A, mark, B, mark, 0.5, mark, mark, C, mark, D, mark, 1.0. Wait, maybe the interval between 0.0 and 0.5 is divided into 4 equal parts? Wait, 0.5 - 0.0 = 0.5, and if there are 4 intervals between 0.0 and 0.5, then each interval is 0.5 / 4 = 0.125? No, that can't be. Wait, no, let's look at the positions. Wait, 0.0, then after 0.0, the first mark: let's say the first interval (0.0 to first mark) is x, then first to A is x, A to second mark is x, second to B is x, B to third mark is x, third to 0.5 is x. Then 5x = 0.5, so x = 0.1? Wait, 5 intervals? Wait, 0.0, then mark1, A, mark2, B, mark3, 0.5. So from 0.0 to 0.5, there are 5 intervals? No, 0.0 to mark1: 1, mark1 to A:2, A to mark2:3, mark2 to B:4, B to mark3:5, mark3 to 0.5:6? No, this is confusing. Wait, maybe the correct way is: 0.4 is less than 0.5, so between 0.0 and 0.5. Let's see the points: A, B, C, D. 0.4 is close to 0.5 but less than 0.5. Let's calculate the value of each point. Let's assume that between 0.0 and 0.5, the intervals are 0.1 each? Wait, 0.0, 0.1, 0.2, 0.3, 0.4, 0.5? Wait, no, the marks: 0.0, then 0.1, A (0.2), 0.3, B (0.4), 0.5. Oh! That makes sense. So 0.0, 0.1, 0.2 (A), 0.3, 0.4 (B), 0.5. Then from 0.5 to 1.0: 0.6, 0.7, 0.8 (C), 0.9, 1.0? Wait, no, D is before 1.0. Wait, but 0.4 is 0.4, which is 0.4, so between 0.0 and 0.5, the values would be 0.0, 0.1, 0.2 (A), 0.3, 0.4 (B), 0.5. So B is at 0.4? Wait, let's check: 0.0 to 0.5, with marks at 0.1, 0.2, 0.3, 0.4. So A is at 0.2, B at 0.4, then 0.5, then 0.6, 0.7, 0.8 (C), 0.9, D at 0.9? No, D is before 1.0. Wait, maybe the interval between 0.0 and 0.5 is 0.5, divided into 5 parts? No, 0.5 / 5 = 0.1, so each part is 0.1. So 0.0 + 0.1 = 0.1, +0.1=0.2 (A), +0.1=0.3, +0.1=0.4 (B), +0.1=0.5. Yes, that makes sense. So each interval is 0.1. So A is at 0.2, B at 0.4, then 0.5, then 0.6, 0.7, 0.8 (C), 0.9, D at 0.9? Wait, no, D is before 1.0, so maybe D is at 0.9? But 0.4 is 0.4, which is B. So the point B is at 0.4.

Step2: Identify the point

Since 0.4 is equal to the value of point B (as calculated by interval length 0.1 between 0.0 and 0.5, with B being 4 intervals from 0.0? Wait, no, 0.0 + 0.14? No, 0.0 + 0.12 is 0.2 (A), 0.0 + 0.1*4 is 0.4 (B). Yes, so B is at 0.4.

Answer:

B. Point B