0.9 Additive Inverse :
The additive inverse of 0.9 is -0.9.
This means that when we add 0.9 and -0.9, the result is zero:
0.9 + (-0.9) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 0.9
- Additive inverse: -0.9
To verify: 0.9 + (-0.9) = 0
Extended Mathematical Exploration of 0.9
Let's explore various mathematical operations and concepts related to 0.9 and its additive inverse -0.9.
Basic Operations and Properties
- Square of 0.9: 0.81
- Cube of 0.9: 0.729
- Square root of |0.9|: 0.94868329805051
- Reciprocal of 0.9: 1.1111111111111
- Double of 0.9: 1.8
- Half of 0.9: 0.45
- Absolute value of 0.9: 0.9
Trigonometric Functions
- Sine of 0.9: 0.78332690962748
- Cosine of 0.9: 0.62160996827066
- Tangent of 0.9: 1.2601582175503
Exponential and Logarithmic Functions
- e^0.9: 2.4596031111569
- Natural log of 0.9: -0.10536051565783
Floor and Ceiling Functions
- Floor of 0.9: 0
- Ceiling of 0.9: 1
Interesting Properties and Relationships
- The sum of 0.9 and its additive inverse (-0.9) is always 0.
- The product of 0.9 and its additive inverse is: -0.81
- The average of 0.9 and its additive inverse is always 0.
- The distance between 0.9 and its additive inverse on a number line is: 1.8
Applications in Algebra
Consider the equation: x + 0.9 = 0
The solution to this equation is x = -0.9, which is the additive inverse of 0.9.
Graphical Representation
On a coordinate plane:
- The point (0.9, 0) is reflected across the y-axis to (-0.9, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 0.9 and Its Additive Inverse
Consider the alternating series: 0.9 + (-0.9) + 0.9 + (-0.9) + ...
The sum of this series oscillates between 0 and 0.9, never converging unless 0.9 is 0.
In Number Theory
For integer values:
- If 0.9 is even, its additive inverse is also even.
- If 0.9 is odd, its additive inverse is also odd.
- The sum of the digits of 0.9 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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