To understand why 2 is 10 times the value of 0.2 using the number line, let's break down the steps in detail:
### Step-by-Step Solution:
1. Identify the Positions of 0.2 and 2 on the Number Line:
- First, let's identify the positions of the numbers 0.2 and 2 on the number line.
- 0.2 is a small positive number, just slightly to the right of 0.
- 2 is a larger positive number, further to the right than 0.2.
2. Visualize 0.2 on the Number Line:
- Start from 0, and move 0.2 units to the right. Mark this position as 0.2.
- On a typical number line with increments of 0.1, this would be the second mark to the right of 0.
3. Visualize 2 on the Number Line:
- From 0, move 2 units to the right. Mark this position as 2.
- On the same number line with increments of 0.1, this would be the twentieth mark to the right of 0.
4. Compare the Position of 0.2 with the Position of 2:
- Notice that moving to 2 from 0 requires ten times the distance moved to reach 0.2 from 0.
- In other words, if you were to repeatedly jump the distance of 0.2 ten times starting from 0, you would end up at the position of 2.
### Mathematical Explanation Using the Number Line:
- Single Step (0.2 to 0.4 to 0.6, etc.):
- Moving in steps of 0.2 on the number line: 0, 0.2, 0.4, 0.6, 0.8, 1.0, 1.2, 1.4, 1.6, 1.8, 2.0.
- Each step represents moving 0.2 units further to the right.
- Ten Steps of 0.2 Equals 2:
- If we take 10 steps of 0.2 units each, we reach 2:
- 0.2 * 10 = 2.0
### Conclusion:
By visualizing the numbers on the number line and understanding the process of repeatedly moving in steps of 0.2, we can see why 2 is 10 times the value of 0.2. Each step of 0.2 adds up, and after 10 steps, we reach the position of 2 on the number line. Therefore, 2 is indeed 10 times the value of 0.2.
