6.9 Additive Inverse :
The additive inverse of 6.9 is -6.9.
This means that when we add 6.9 and -6.9, the result is zero:
6.9 + (-6.9) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 6.9
- Additive inverse: -6.9
To verify: 6.9 + (-6.9) = 0
Extended Mathematical Exploration of 6.9
Let's explore various mathematical operations and concepts related to 6.9 and its additive inverse -6.9.
Basic Operations and Properties
- Square of 6.9: 47.61
- Cube of 6.9: 328.509
- Square root of |6.9|: 2.6267851073127
- Reciprocal of 6.9: 0.14492753623188
- Double of 6.9: 13.8
- Half of 6.9: 3.45
- Absolute value of 6.9: 6.9
Trigonometric Functions
- Sine of 6.9: 0.5784397643882
- Cosine of 6.9: 0.81572510012536
- Tangent of 6.9: 0.70911115067969
Exponential and Logarithmic Functions
- e^6.9: 992.27471560503
- Natural log of 6.9: 1.9315214116032
Floor and Ceiling Functions
- Floor of 6.9: 6
- Ceiling of 6.9: 7
Interesting Properties and Relationships
- The sum of 6.9 and its additive inverse (-6.9) is always 0.
- The product of 6.9 and its additive inverse is: -47.61
- The average of 6.9 and its additive inverse is always 0.
- The distance between 6.9 and its additive inverse on a number line is: 13.8
Applications in Algebra
Consider the equation: x + 6.9 = 0
The solution to this equation is x = -6.9, which is the additive inverse of 6.9.
Graphical Representation
On a coordinate plane:
- The point (6.9, 0) is reflected across the y-axis to (-6.9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 6.9 and Its Additive Inverse
Consider the alternating series: 6.9 + (-6.9) + 6.9 + (-6.9) + ...
The sum of this series oscillates between 0 and 6.9, never converging unless 6.9 is 0.
In Number Theory
For integer values:
- If 6.9 is even, its additive inverse is also even.
- If 6.9 is odd, its additive inverse is also odd.
- The sum of the digits of 6.9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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