Understanding -1 on the Number Line
The concept of -1 on a number line represents a specific point that is one unit to the left of 0. Here’s a detailed breakdown:
Number Line Representation
- A number line is a straight line with numbers placed at equal intervals.
- The center of the number line is 0, with positive numbers extending to the right and negative numbers extending to the left.
- -1 is the first negative integer and is found directly to the left of 0.
Visualizing -1
- Imagine moving left from 0, each step represents a decrease by 1.
- The sequence goes: 0, -1, -2, -3, etc.
- This helps in understanding the position and value of negative integers.
Rational Numbers Between Two Rational Numbers
Rational numbers are numbers that can be expressed as a fraction of two integers.
- Between any two rational numbers, there always exists another rational number.
- For example, between -1 and 0, we can find -0.5, which is also a rational number.
- The existence of rational numbers between any two given rational numbers demonstrates the density of rational numbers on the number line.
Examples of Rational Numbers
- If we take -1 and 1, the following are some rational numbers that lie between them:
- 0
- 0.5
- -0.5
- This showcases that between any two numbers, there are infinitely many rational numbers.
This understanding of -1 and rational numbers is fundamental in mathematics, especially when dealing with number lines and comparisons.