6.75 Additive Inverse :
The additive inverse of 6.75 is -6.75.
This means that when we add 6.75 and -6.75, the result is zero:
6.75 + (-6.75) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 6.75
- Additive inverse: -6.75
To verify: 6.75 + (-6.75) = 0
Extended Mathematical Exploration of 6.75
Let's explore various mathematical operations and concepts related to 6.75 and its additive inverse -6.75.
Basic Operations and Properties
- Square of 6.75: 45.5625
- Cube of 6.75: 307.546875
- Square root of |6.75|: 2.5980762113533
- Reciprocal of 6.75: 0.14814814814815
- Double of 6.75: 13.5
- Half of 6.75: 3.375
- Absolute value of 6.75: 6.75
Trigonometric Functions
- Sine of 6.75: 0.45004407378062
- Cosine of 6.75: 0.89300634468908
- Tangent of 6.75: 0.50396514700835
Exponential and Logarithmic Functions
- e^6.75: 854.05876252615
- Natural log of 6.75: 1.9095425048844
Floor and Ceiling Functions
- Floor of 6.75: 6
- Ceiling of 6.75: 7
Interesting Properties and Relationships
- The sum of 6.75 and its additive inverse (-6.75) is always 0.
- The product of 6.75 and its additive inverse is: -45.5625
- The average of 6.75 and its additive inverse is always 0.
- The distance between 6.75 and its additive inverse on a number line is: 13.5
Applications in Algebra
Consider the equation: x + 6.75 = 0
The solution to this equation is x = -6.75, which is the additive inverse of 6.75.
Graphical Representation
On a coordinate plane:
- The point (6.75, 0) is reflected across the y-axis to (-6.75, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 6.75 and Its Additive Inverse
Consider the alternating series: 6.75 + (-6.75) + 6.75 + (-6.75) + ...
The sum of this series oscillates between 0 and 6.75, never converging unless 6.75 is 0.
In Number Theory
For integer values:
- If 6.75 is even, its additive inverse is also even.
- If 6.75 is odd, its additive inverse is also odd.
- The sum of the digits of 6.75 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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