12.4 Additive Inverse :
The additive inverse of 12.4 is -12.4.
This means that when we add 12.4 and -12.4, the result is zero:
12.4 + (-12.4) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 12.4
- Additive inverse: -12.4
To verify: 12.4 + (-12.4) = 0
Extended Mathematical Exploration of 12.4
Let's explore various mathematical operations and concepts related to 12.4 and its additive inverse -12.4.
Basic Operations and Properties
- Square of 12.4: 153.76
- Cube of 12.4: 1906.624
- Square root of |12.4|: 3.5213633723318
- Reciprocal of 12.4: 0.080645161290323
- Double of 12.4: 24.8
- Half of 12.4: 6.2
- Absolute value of 12.4: 12.4
Trigonometric Functions
- Sine of 12.4: -0.16560417544831
- Cosine of 12.4: 0.98619230227886
- Tangent of 12.4: -0.16792280274916
Exponential and Logarithmic Functions
- e^12.4: 242801.61749832
- Natural log of 12.4: 2.517696472611
Floor and Ceiling Functions
- Floor of 12.4: 12
- Ceiling of 12.4: 13
Interesting Properties and Relationships
- The sum of 12.4 and its additive inverse (-12.4) is always 0.
- The product of 12.4 and its additive inverse is: -153.76
- The average of 12.4 and its additive inverse is always 0.
- The distance between 12.4 and its additive inverse on a number line is: 24.8
Applications in Algebra
Consider the equation: x + 12.4 = 0
The solution to this equation is x = -12.4, which is the additive inverse of 12.4.
Graphical Representation
On a coordinate plane:
- The point (12.4, 0) is reflected across the y-axis to (-12.4, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 12.4 and Its Additive Inverse
Consider the alternating series: 12.4 + (-12.4) + 12.4 + (-12.4) + ...
The sum of this series oscillates between 0 and 12.4, never converging unless 12.4 is 0.
In Number Theory
For integer values:
- If 12.4 is even, its additive inverse is also even.
- If 12.4 is odd, its additive inverse is also odd.
- The sum of the digits of 12.4 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: