12.5 Additive Inverse :
The additive inverse of 12.5 is -12.5.
This means that when we add 12.5 and -12.5, the result is zero:
12.5 + (-12.5) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 12.5
- Additive inverse: -12.5
To verify: 12.5 + (-12.5) = 0
Extended Mathematical Exploration of 12.5
Let's explore various mathematical operations and concepts related to 12.5 and its additive inverse -12.5.
Basic Operations and Properties
- Square of 12.5: 156.25
- Cube of 12.5: 1953.125
- Square root of |12.5|: 3.5355339059327
- Reciprocal of 12.5: 0.08
- Double of 12.5: 25
- Half of 12.5: 6.25
- Absolute value of 12.5: 12.5
Trigonometric Functions
- Sine of 12.5: -0.066321897351201
- Cosine of 12.5: 0.99779827917858
- Tangent of 12.5: -0.066468241863274
Exponential and Logarithmic Functions
- e^12.5: 268337.28652087
- Natural log of 12.5: 2.5257286443083
Floor and Ceiling Functions
- Floor of 12.5: 12
- Ceiling of 12.5: 13
Interesting Properties and Relationships
- The sum of 12.5 and its additive inverse (-12.5) is always 0.
- The product of 12.5 and its additive inverse is: -156.25
- The average of 12.5 and its additive inverse is always 0.
- The distance between 12.5 and its additive inverse on a number line is: 25
Applications in Algebra
Consider the equation: x + 12.5 = 0
The solution to this equation is x = -12.5, which is the additive inverse of 12.5.
Graphical Representation
On a coordinate plane:
- The point (12.5, 0) is reflected across the y-axis to (-12.5, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 12.5 and Its Additive Inverse
Consider the alternating series: 12.5 + (-12.5) + 12.5 + (-12.5) + ...
The sum of this series oscillates between 0 and 12.5, never converging unless 12.5 is 0.
In Number Theory
For integer values:
- If 12.5 is even, its additive inverse is also even.
- If 12.5 is odd, its additive inverse is also odd.
- The sum of the digits of 12.5 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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