1/10 Additive Inverse :
The additive inverse of 1/10 is -1/10.
This means that when we add 1/10 and -1/10, the result is zero:
1/10 + (-1/10) = 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: 1/10
- Additive inverse: -1/10
To verify: 1/10 + (-1/10) = 0
Extended Mathematical Exploration of 1/10
Let's explore various mathematical operations and concepts related to 1/10 and its additive inverse -1/10.
Basic Operations and Properties
- Square of 1/10: 0.01
- Cube of 1/10: 0.001
- Square root of |1/10|: 0.31622776601684
- Reciprocal of 1/10: 10
- Double of 1/10: 0.2
- Half of 1/10: 0.05
- Absolute value of 1/10: 0.1
Trigonometric Functions
- Sine of 1/10: 0.099833416646828
- Cosine of 1/10: 0.99500416527803
- Tangent of 1/10: 0.10033467208545
Exponential and Logarithmic Functions
- e^1/10: 1.1051709180756
- Natural log of 1/10: -2.302585092994
Floor and Ceiling Functions
- Floor of 1/10: 0
- Ceiling of 1/10: 1
Interesting Properties and Relationships
- The sum of 1/10 and its additive inverse (-1/10) is always 0.
- The product of 1/10 and its additive inverse is: -1
- The average of 1/10 and its additive inverse is always 0.
- The distance between 1/10 and its additive inverse on a number line is: 2
Applications in Algebra
Consider the equation: x + 1/10 = 0
The solution to this equation is x = -1/10, which is the additive inverse of 1/10.
Graphical Representation
On a coordinate plane:
- The point (1/10, 0) is reflected across the y-axis to (-1/10, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1/10 and Its Additive Inverse
Consider the alternating series: 1/10 + (-1/10) + 1/10 + (-1/10) + ...
The sum of this series oscillates between 0 and 1/10, never converging unless 1/10 is 0.
In Number Theory
For integer values:
- If 1/10 is even, its additive inverse is also even.
- If 1/10 is odd, its additive inverse is also odd.
- The sum of the digits of 1/10 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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