10.2 Additive Inverse :
The additive inverse of 10.2 is -10.2.
This means that when we add 10.2 and -10.2, the result is zero:
10.2 + (-10.2) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 10.2
- Additive inverse: -10.2
To verify: 10.2 + (-10.2) = 0
Extended Mathematical Exploration of 10.2
Let's explore various mathematical operations and concepts related to 10.2 and its additive inverse -10.2.
Basic Operations and Properties
- Square of 10.2: 104.04
- Cube of 10.2: 1061.208
- Square root of |10.2|: 3.1937438845343
- Reciprocal of 10.2: 0.098039215686275
- Double of 10.2: 20.4
- Half of 10.2: 5.1
- Absolute value of 10.2: 10.2
Trigonometric Functions
- Sine of 10.2: -0.69987468759354
- Cosine of 10.2: -0.7142656520272
- Tangent of 10.2: 0.9798520838951
Exponential and Logarithmic Functions
- e^10.2: 26903.186074298
- Natural log of 10.2: 2.3223877202902
Floor and Ceiling Functions
- Floor of 10.2: 10
- Ceiling of 10.2: 11
Interesting Properties and Relationships
- The sum of 10.2 and its additive inverse (-10.2) is always 0.
- The product of 10.2 and its additive inverse is: -104.04
- The average of 10.2 and its additive inverse is always 0.
- The distance between 10.2 and its additive inverse on a number line is: 20.4
Applications in Algebra
Consider the equation: x + 10.2 = 0
The solution to this equation is x = -10.2, which is the additive inverse of 10.2.
Graphical Representation
On a coordinate plane:
- The point (10.2, 0) is reflected across the y-axis to (-10.2, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 10.2 and Its Additive Inverse
Consider the alternating series: 10.2 + (-10.2) + 10.2 + (-10.2) + ...
The sum of this series oscillates between 0 and 10.2, never converging unless 10.2 is 0.
In Number Theory
For integer values:
- If 10.2 is even, its additive inverse is also even.
- If 10.2 is odd, its additive inverse is also odd.
- The sum of the digits of 10.2 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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