Question

which shows -0.2 graphed on the number line? (four number lines are shown, each with ticks at -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 and a purple dot at different positions: first at -3, second between -1 and 0, third at 0, fourth at -1)

Explanation:

Step1: Understand -0.2's position

-0.2 is a negative number, so it's to the left of 0. It's between -1 and 0, closer to 0 (since 0.2 is 1/5 of the way from 0 to -1? Wait, no: the distance from 0 to -1 is 1 unit. -0.2 is 0.2 units left of 0, so between 0 and -1, closer to 0.

Step2: Analyze each number line

• First number line: dot at -3 → too far left.
• Second number line: dot between -1 and 0, closer to 0? Wait, let's check the ticks. The second number line has a dot between -1 and 0? Wait, no, the second number line's dot is between -1 and 0? Wait, the third number line: dot at 0? No, third is at 0? Wait, no, the third number line's dot is at 0? Wait, no, let's re-examine.

Wait, the four number lines:

1. First: dot at -3.
2. Second: dot between -1 and 0 (closer to 0? Wait, the tick marks: each major tick is integer. So between -1 and 0, the midpoint is -0.5, but -0.2 is closer to 0 than to -1. Wait, the second number line's dot is between -1 and 0, closer to 0? Wait, no, the second number line: the dot is at a position between -1 and 0, maybe at -0.2? Wait, the third number line: dot at 0? No, third is at 0? Wait, no, the third number line's dot is at 0? Wait, no, the third number line: the dot is at 0? Wait, no, the third number line: the dot is at 0? Wait, no, let's look again.

Wait, the second number line: the dot is between -1 and 0, closer to 0. The third number line: dot at 0? No, third is at 0? Wait, no, the third number line's dot is at 0? Wait, no, the third number line: the dot is at 0? Wait, no, the third number line: the dot is at 0? Wait, no, the fourth number line: dot at -1.

Wait, no, let's list each:

1. First: dot at -3 (major tick -3)
2. Second: dot between -1 and 0 (so between -1 and 0, which is where -0.2 is)
3. Third: dot at 0 (major tick 0)
4. Fourth: dot at -1 (major tick -1)

So -0.2 is between -1 and 0, closer to 0. So the second number line (the middle one? Wait, the four are: first, second, third, fourth. Wait, the user's image: four number lines? Wait, the original problem has four? Wait, the user's image:

First number line: ticks at -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Dot at -3.

Second number line: same ticks, dot between -1 and 0 (so between -1 and 0, which is the interval for -0.2).

Third number line: dot at 0.

Fourth number line: dot at -1.

So -0.2 is between -1 and 0, so the second number line (the one with the dot between -1 and 0) is correct. Wait, but let's confirm: -0.2 is greater than -1 (since -0.2 > -1) and less than 0 (since -0.2 < 0). So it's in the interval (-1, 0). So the second number line (the middle one, the second of the four) has the dot in that interval. So the correct one is the second number line (the one with the dot between -1 and 0).

Wait, but the user's image: maybe the second number line is the one with the dot between -1 and 0. So the answer is the second number line (the middle one, or the second from the top).

Answer:

The second number line (the one with the dot between -1 and 0, closer to 0)