Question

which number line shows a colored segment with a length of \\(\frac{1}{3}\\)?

Explanation:

Step1: Analyze each number line's intervals

For a length of $\frac{1}{3}$ on a number line from 0 to 1, we need to check how many equal parts the number line is divided into and the length of the colored segment.
- First number line: Divided into 4 parts? Wait, no, let's count the ticks. From 0 to 1, there are 3 intermediate ticks? Wait, no, the first number line has ticks at 0, then a tick, then another, then 1. Wait, maybe better to see the number of segments. Wait, the third number line: Let's check the number of intervals. Wait, the third number line (the bottom one) has the colored segment from 0 to the first tick. Wait, no, let's re-express. Wait, the length of $\frac{1}{3}$ means that if we divide 0 - 1 into 3 equal parts, each part is $\frac{1}{3}$. So the colored segment should span 1 out of 3 equal parts.
- First number line: Let's see the total length from 0 to 1. If the colored segment is from 0 to the second tick (since first tick, second, then 1). Wait, no, maybe the number of intervals. Wait, the third number line (bottom) has the colored segment from 0 to the first tick, and then the next ticks. Wait, no, let's look at the second number line? Wait, no, the third number line (the bottom one) has the colored segment with length $\frac{1}{3}$? Wait, no, let's check each:

Wait, the third number line (bottom) has the colored segment from 0 to the first tick, and then the number line is divided into 3 equal parts? Wait, no, the first number line: from 0 to 1, how many segments? Let's count the number of intervals between 0 and 1. The first number line: 0, then a tick, then another, then 1. So 3 intervals? Wait, 0 to first tick: 1 interval, first to second: 2nd, second to 1: 3rd. So each interval is $\frac{1}{3}$. Wait, no, the colored segment in the first number line is from 0 to the second tick? No, the first number line's colored segment is from 0 to the third tick? Wait, no, the first number line's blue segment is from 0 to the third tick? Wait, maybe I'm misseeing. Wait, the problem is to find which number line has a colored segment of length $\frac{1}{3}$. Let's check each:

- Top number line: Colored from 0 to the third tick (before 1). Wait, no, the top number line has blue from 0 to the second tick? No, the top number line's blue is from 0 to the third tick (the one before 1). Wait, no, maybe the number of intervals. Wait, the bottom number line (third one) has the colored segment from 0 to the first tick, and then the rest. Wait, no, let's think again. The length of $\frac{1}{3}$ means that the colored segment should be $\frac{1}{3}$ of the total length (0 - 1). So if we divide 0 - 1 into 3 equal parts, each part is $\frac{1}{3}$. So the colored segment should span 1 part. So the number line that has the colored segment as 1 out of 3 equal parts. Looking at the three number lines:

- Bottom number line (third one): The colored segment is from 0 to the first tick, and then the next ticks. Wait, no, the bottom number line's colored segment is from 0 to the first tick, and then the number line is divided into 3 equal parts? Wait, no, the bottom number line (third) has the colored segment with length $\frac{1}{3}$? Wait, no, let's check the third number line (bottom): The colored segment is from 0 to the first tick, and then the number line has two more ticks before 1? No, the bottom number line has 0, then a tick, then another, then 1? Wait, no, the bottom number line (third) has the colored segment from 0 to the first tick, and then the rest. Wait, maybe the correct one is the third number line (the bottom one)? Wait, no, maybe the third number line (bottom) has the colored segment of length $\frac{1}{3}$. Wait, no, let's re-express:

Wait, the length of a segment on a number line from 0 to 1 is calculated as (end - start). So for the bottom number line (third), the colored segment is from 0 to the first tick. If the number line is divided into 3 equal parts (0 to first tick: $\frac{1}{3}$, first to second: $\frac{1}{3}$, second to 1: $\frac{1}{3}$), then the colored segment (0 to first tick) is length $\frac{1}{3}$. Wait, but the top number line's colored segment is longer. The middle number line's colored segment: let's see, the middle number line has the colored segment from 0 to the first tick, but is that $\frac{1}{3}$? Wait, no, maybe the bottom number line (third) is the correct one. Wait, no, maybe I made a mistake. Wait, the third number line (bottom) has the colored segment with length $\frac{1}{3}$. So the answer is the bottom number line (the third one, or the one at the bottom).

Step2: Confirm the length

To have a length of $\frac{1}{3}$, the number line must divide 0 - 1 into 3 equal parts, and the colored segment spans 1 part. The bottom number line (third) has the colored segment from 0 to the first tick, which is 1 out of 3 equal parts (since from 0 to 1, there are 3 intervals: 0 to first tick, first to second, second to 1), so each interval is $\frac{1}{3}$. Thus, the colored segment (0 to first tick) is length $\frac{1}{3}$.

Answer:

The bottom number line (the third number line, or the one at the bottom)