Question

question 1 of 8
which expression is represented on the number line?
number line with markings -1.2, -0.8, -0.4, 0, 0.4, 0.8, 1.2 and red arrows from -0.2 to -0.4, -0.4 to -0.6? wait, looking at the number line: the red arrows seem to be moving from 0 towards negative, with steps. wait the options are: -0.6·3, -0.2·3, -0.2·(-3), -0.6·(-3)
options:

• -0.6 · 3
• -0.2 · 3
• -0.2 · (-3)
• -0.6 · (-3)

Explanation:

Step1: Analyze the number line movement

The number line has arrows moving from 0 to -0.2 (wait, no, looking at the intervals: the distance between -0.4 and 0 is 0.4, divided into two parts? Wait, no, the marks are at -1.2, -0.8, -0.4, 0, 0.4, 0.8, 1.2. So each interval between marks is 0.4? Wait, no, from -1.2 to -0.8 is 0.4, -0.8 to -0.4 is 0.4, -0.4 to 0 is 0.4, etc. Wait, the red arrows: let's see the starting point? Wait, maybe the movement is 3 times of -0.2? Wait, no, let's check the options. Wait, the options are multiplications. Let's calculate each option:

Option 1: \(-0.6 \cdot 3 = -1.8\) (not matching the number line, since the number line goes to -1.2)
Option 2: \(-0.2 \cdot 3 = -0.6\)? Wait, no, wait the number line: from 0, moving left 3 times, each time 0.2? Wait, the marks: -0.4, -0.8, -1.2? Wait, no, the number line has -1.2, -0.8, -0.4, 0, 0.4, 0.8, 1.2. So the distance between -0.4 and 0 is 0.4, so each small segment? Wait, maybe the arrows are moving from 0 to -0.2, then -0.2 to -0.4, then -0.4 to -0.6? Wait, no, the red arrows: let's count the steps. Wait, the number line: the first arrow starts at 0, goes to -0.2? No, maybe the intervals between the marks: from -1.2 to -0.8 is 0.4, so each mark is 0.4 apart? Wait, no, -1.2, -0.8 (difference 0.4), -0.8 to -0.4 (0.4), -0.4 to 0 (0.4), 0 to 0.4 (0.4), etc. So the red arrows: how many steps? Let's see the number of red arrows: 3 arrows. Each arrow's length: from 0 to -0.2? No, wait the options are multiplications. Let's check each option:

Option A: \(-0.6 \times 3 = -1.8\) (too far left, number line only to -1.2)
Option B: \(-0.2 \times 3 = -0.6\)? Wait, no, -0.2*3 is -0.6, but the number line has -0.4, -0.8, -1.2. Wait, maybe I misread the number line. Wait, the number line: the marks are -1.2, -0.8, -0.4, 0, 0.4, 0.8, 1.2. So the distance between -0.4 and 0 is 0.4, so each mark is 0.4 units apart. Wait, the red arrows: let's see the starting point. Wait, maybe the expression is -0.2 * 3? Wait, no, -0.2*3 is -0.6, but the number line has -0.4, -0.8, -1.2. Wait, maybe the arrows are moving from 0 to -0.2, then -0.2 to -0.4, then -0.4 to -0.6? No, the number line doesn't have -0.6. Wait, maybe the number line's marks are -1.2, -0.8, -0.4, 0, 0.4, 0.8, 1.2, so each mark is 0.4 units. So the length between 0 and -0.4 is 0.4, so each small segment is 0.2? Wait, 0 to -0.4 is 0.4, so two segments of 0.2 each. So the red arrows: three arrows, each of length 0.2, moving left (negative direction). So total movement is 3 * (-0.2) = -0.6? Wait, no, -0.2*3 is -0.6, but the number line has -0.4, -0.8, -1.2. Wait, maybe the options are different. Wait, the options:

Wait, the options are:

1. \(-0.6 \cdot 3\)
2. \(-0.2 \cdot 3\)
3. \(-0.2 \cdot (-3)\)
4. \(-0.6 \cdot (-3)\)

Wait, let's calculate each:

1. \(-0.6 \times 3 = -1.8\) (not on the number line, since the leftmost is -1.2)
2. \(-0.2 \times 3 = -0.6\) (but the number line has -0.4, -0.8, -1.2. Wait, maybe the number line's marks are -1.2, -0.8, -0.4, 0, so -0.4 is one mark, -0.8 is another, -1.2 is another. Wait, -0.2*3 is -0.6, which is between -0.4 and -0.8? No, -0.6 is between -0.4 (-0.4) and -0.8 (-0.8)? Wait, -0.6 is less than -0.4 and greater than -0.8. Wait, maybe the number line's scale is different. Wait, maybe the distance between -0.4 and 0 is 0.4, so each unit is 0.4? No, that doesn't make sense. Wait, maybe the red arrows are moving from 0 to -0.2, then -0.2 to -0.4, then -0.4 to -0.6? But the number line has -0.4, -0.8, -1.2. Wait, maybe I made a mistake. Wait, let's check the options again. Wait, the third option is \(-0.2 \cdot (-3) = 0.6\) (positive, so right direction, but the arrows are left, so no). Fourth option: \(-0.6 \cdot (-3) = 1.8\) (positive, no). First option: -1.8 (too left). Second option: -0.6. Wait, maybe the number line's marks are -1.2, -0.8, -0.4, 0, so -0.6 is between -0.4 and -0.8? Wait, -0.4 is to the right of -0.8, so -0.6 is between -0.4 (which is -0.4) and -0.8 (which is -0.8)? No, -0.6 is greater than -0.8 and less than -0.4. So -0.6 is between -0.8 and -0.4. So the number line has -1.2, -0.8, -0.4, 0. So -0.6 is between -0.8 and -0.4. So the red arrows: three steps, each of 0.2, so 3*(-0.2) = -0.6. So the correct option is \(-0.2 \cdot 3\).

Wait, but let's confirm:

-0.2 * 3 = -0.6. The number line has -0.8, -0.4, so -0.6 is between them. The arrows are moving left (negative direction) three times, each time 0.2 units. So that's -0.2 * 3.

Step2: Verify each option

- Option 1: \(-0.6 \times 3 = -1.8\) (too far left, number line ends at -1.2) → Incorrect.
- Option 2: \(-0.2 \times 3 = -0.6\) (matches the movement: 3 times left 0.2) → Correct.
- Option 3: \(-0.2 \times (-3) = 0.6\) (positive, right direction, arrows are left) → Incorrect.
- Option 4: \(-0.6 \times (-3) = 1.8\) (positive, right direction) → Incorrect.

Answer:

\(\boldsymbol{-0.2 \cdot 3}\) (the option corresponding to this expression, likely option B if options are labeled A, B, C, D as per typical multiple-choice, but based on the calculation, the expression is \(-0.2 \cdot 3\))