13.4 Additive Inverse :
The additive inverse of 13.4 is -13.4.
This means that when we add 13.4 and -13.4, the result is zero:
13.4 + (-13.4) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 13.4
- Additive inverse: -13.4
To verify: 13.4 + (-13.4) = 0
Extended Mathematical Exploration of 13.4
Let's explore various mathematical operations and concepts related to 13.4 and its additive inverse -13.4.
Basic Operations and Properties
- Square of 13.4: 179.56
- Cube of 13.4: 2406.104
- Square root of |13.4|: 3.6606010435446
- Reciprocal of 13.4: 0.074626865671642
- Double of 13.4: 26.8
- Half of 13.4: 6.7
- Absolute value of 13.4: 13.4
Trigonometric Functions
- Sine of 13.4: 0.74037588995245
- Cosine of 13.4: 0.67219308355347
- Tangent of 13.4: 1.1014333650066
Exponential and Logarithmic Functions
- e^13.4: 660003.22476616
- Natural log of 13.4: 2.5952547069569
Floor and Ceiling Functions
- Floor of 13.4: 13
- Ceiling of 13.4: 14
Interesting Properties and Relationships
- The sum of 13.4 and its additive inverse (-13.4) is always 0.
- The product of 13.4 and its additive inverse is: -179.56
- The average of 13.4 and its additive inverse is always 0.
- The distance between 13.4 and its additive inverse on a number line is: 26.8
Applications in Algebra
Consider the equation: x + 13.4 = 0
The solution to this equation is x = -13.4, which is the additive inverse of 13.4.
Graphical Representation
On a coordinate plane:
- The point (13.4, 0) is reflected across the y-axis to (-13.4, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 13.4 and Its Additive Inverse
Consider the alternating series: 13.4 + (-13.4) + 13.4 + (-13.4) + ...
The sum of this series oscillates between 0 and 13.4, never converging unless 13.4 is 0.
In Number Theory
For integer values:
- If 13.4 is even, its additive inverse is also even.
- If 13.4 is odd, its additive inverse is also odd.
- The sum of the digits of 13.4 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: