8.4 Additive Inverse :
The additive inverse of 8.4 is -8.4.
This means that when we add 8.4 and -8.4, the result is zero:
8.4 + (-8.4) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 8.4
- Additive inverse: -8.4
To verify: 8.4 + (-8.4) = 0
Extended Mathematical Exploration of 8.4
Let's explore various mathematical operations and concepts related to 8.4 and its additive inverse -8.4.
Basic Operations and Properties
- Square of 8.4: 70.56
- Cube of 8.4: 592.704
- Square root of |8.4|: 2.8982753492379
- Reciprocal of 8.4: 0.11904761904762
- Double of 8.4: 16.8
- Half of 8.4: 4.2
- Absolute value of 8.4: 8.4
Trigonometric Functions
- Sine of 8.4: 0.85459890808828
- Cosine of 8.4: -0.51928865411669
- Tangent of 8.4: -1.6457107262279
Exponential and Logarithmic Functions
- e^8.4: 4447.0667476999
- Natural log of 8.4: 2.1282317058493
Floor and Ceiling Functions
- Floor of 8.4: 8
- Ceiling of 8.4: 9
Interesting Properties and Relationships
- The sum of 8.4 and its additive inverse (-8.4) is always 0.
- The product of 8.4 and its additive inverse is: -70.56
- The average of 8.4 and its additive inverse is always 0.
- The distance between 8.4 and its additive inverse on a number line is: 16.8
Applications in Algebra
Consider the equation: x + 8.4 = 0
The solution to this equation is x = -8.4, which is the additive inverse of 8.4.
Graphical Representation
On a coordinate plane:
- The point (8.4, 0) is reflected across the y-axis to (-8.4, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 8.4 and Its Additive Inverse
Consider the alternating series: 8.4 + (-8.4) + 8.4 + (-8.4) + ...
The sum of this series oscillates between 0 and 8.4, never converging unless 8.4 is 0.
In Number Theory
For integer values:
- If 8.4 is even, its additive inverse is also even.
- If 8.4 is odd, its additive inverse is also odd.
- The sum of the digits of 8.4 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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