9/10 Additive Inverse :
The additive inverse of 9/10 is -9/10.
This means that when we add 9/10 and -9/10, the result is zero:
9/10 + (-9/10) = 0
Additive Inverse of a Fraction
For fractions, the additive inverse is found by negating the numerator or denominator, but not both. In this case:
- Original fraction: 9/10
- Additive inverse: -9/10
To verify: 9/10 + (-9/10) = 0
Extended Mathematical Exploration of 9/10
Let's explore various mathematical operations and concepts related to 9/10 and its additive inverse -9/10.
Basic Operations and Properties
- Square of 9/10: 0.81
- Cube of 9/10: 0.729
- Square root of |9/10|: 0.94868329805051
- Reciprocal of 9/10: 1.1111111111111
- Double of 9/10: 1.8
- Half of 9/10: 0.45
- Absolute value of 9/10: 0.9
Trigonometric Functions
- Sine of 9/10: 0.78332690962748
- Cosine of 9/10: 0.62160996827066
- Tangent of 9/10: 1.2601582175503
Exponential and Logarithmic Functions
- e^9/10: 2.4596031111569
- Natural log of 9/10: -0.10536051565783
Floor and Ceiling Functions
- Floor of 9/10: 0
- Ceiling of 9/10: 1
Interesting Properties and Relationships
- The sum of 9/10 and its additive inverse (-9/10) is always 0.
- The product of 9/10 and its additive inverse is: -81
- The average of 9/10 and its additive inverse is always 0.
- The distance between 9/10 and its additive inverse on a number line is: 18
Applications in Algebra
Consider the equation: x + 9/10 = 0
The solution to this equation is x = -9/10, which is the additive inverse of 9/10.
Graphical Representation
On a coordinate plane:
- The point (9/10, 0) is reflected across the y-axis to (-9/10, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 9/10 and Its Additive Inverse
Consider the alternating series: 9/10 + (-9/10) + 9/10 + (-9/10) + ...
The sum of this series oscillates between 0 and 9/10, never converging unless 9/10 is 0.
In Number Theory
For integer values:
- If 9/10 is even, its additive inverse is also even.
- If 9/10 is odd, its additive inverse is also odd.
- The sum of the digits of 9/10 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
Enter a number (whole number, decimal, or fraction) to find its additive inverse: