10.8 Additive Inverse :
The additive inverse of 10.8 is -10.8.
This means that when we add 10.8 and -10.8, the result is zero:
10.8 + (-10.8) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 10.8
- Additive inverse: -10.8
To verify: 10.8 + (-10.8) = 0
Extended Mathematical Exploration of 10.8
Let's explore various mathematical operations and concepts related to 10.8 and its additive inverse -10.8.
Basic Operations and Properties
- Square of 10.8: 116.64
- Cube of 10.8: 1259.712
- Square root of |10.8|: 3.286335345031
- Reciprocal of 10.8: 0.092592592592593
- Double of 10.8: 21.6
- Half of 10.8: 5.4
- Absolute value of 10.8: 10.8
Trigonometric Functions
- Sine of 10.8: -0.98093623006649
- Cosine of 10.8: -0.19432990645533
- Tangent of 10.8: 5.0477883098861
Exponential and Logarithmic Functions
- e^10.8: 49020.801136382
- Natural log of 10.8: 2.3795461341302
Floor and Ceiling Functions
- Floor of 10.8: 10
- Ceiling of 10.8: 11
Interesting Properties and Relationships
- The sum of 10.8 and its additive inverse (-10.8) is always 0.
- The product of 10.8 and its additive inverse is: -116.64
- The average of 10.8 and its additive inverse is always 0.
- The distance between 10.8 and its additive inverse on a number line is: 21.6
Applications in Algebra
Consider the equation: x + 10.8 = 0
The solution to this equation is x = -10.8, which is the additive inverse of 10.8.
Graphical Representation
On a coordinate plane:
- The point (10.8, 0) is reflected across the y-axis to (-10.8, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10.8 and Its Additive Inverse
Consider the alternating series: 10.8 + (-10.8) + 10.8 + (-10.8) + ...
The sum of this series oscillates between 0 and 10.8, never converging unless 10.8 is 0.
In Number Theory
For integer values:
- If 10.8 is even, its additive inverse is also even.
- If 10.8 is odd, its additive inverse is also odd.
- The sum of the digits of 10.8 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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