Integers are represented on a number line as points positioned at equal intervals, with positive integers to the right of zero and negative integers to the left.
Here's a breakdown:
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The Number Line: A number line is a visual representation of numbers as points on a straight line.
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Zero as the Origin: The number zero (0) is the central point, acting as the origin.
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Positive Integers: Positive integers (1, 2, 3, ...) are placed to the right of zero. The distance between 0 and 1 is the same as the distance between 1 and 2, and so on. These represent whole numbers greater than zero.
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Negative Integers: Negative integers (-1, -2, -3, ...) are placed to the left of zero. The distance between 0 and -1 is the same as the distance between -1 and -2, and so on. These represent whole numbers less than zero.
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Equal Intervals: The key is that the spacing between consecutive integers is always equal. This ensures an accurate visual representation of their relative values.
Example:
Imagine a number line.
- 0 is in the middle.
- 1 is one unit to the right of 0.
- 2 is one unit to the right of 1 (and two units to the right of 0).
- -1 is one unit to the left of 0.
- -2 is one unit to the left of -1 (and two units to the left of 0).
Therefore, integers on a number line are discrete points equally spaced on either side of zero, providing a visual order and comparison of their values.
