6.7 Additive Inverse :
The additive inverse of 6.7 is -6.7.
This means that when we add 6.7 and -6.7, the result is zero:
6.7 + (-6.7) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 6.7
- Additive inverse: -6.7
To verify: 6.7 + (-6.7) = 0
Extended Mathematical Exploration of 6.7
Let's explore various mathematical operations and concepts related to 6.7 and its additive inverse -6.7.
Basic Operations and Properties
- Square of 6.7: 44.89
- Cube of 6.7: 300.763
- Square root of |6.7|: 2.588435821109
- Reciprocal of 6.7: 0.14925373134328
- Double of 6.7: 13.4
- Half of 6.7: 3.35
- Absolute value of 6.7: 6.7
Trigonometric Functions
- Sine of 6.7: 0.4048499206166
- Cosine of 6.7: 0.91438314823532
- Tangent of 6.7: 0.44275741673272
Exponential and Logarithmic Functions
- e^6.7: 812.40582516754
- Natural log of 6.7: 1.9021075263969
Floor and Ceiling Functions
- Floor of 6.7: 6
- Ceiling of 6.7: 7
Interesting Properties and Relationships
- The sum of 6.7 and its additive inverse (-6.7) is always 0.
- The product of 6.7 and its additive inverse is: -44.89
- The average of 6.7 and its additive inverse is always 0.
- The distance between 6.7 and its additive inverse on a number line is: 13.4
Applications in Algebra
Consider the equation: x + 6.7 = 0
The solution to this equation is x = -6.7, which is the additive inverse of 6.7.
Graphical Representation
On a coordinate plane:
- The point (6.7, 0) is reflected across the y-axis to (-6.7, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 6.7 and Its Additive Inverse
Consider the alternating series: 6.7 + (-6.7) + 6.7 + (-6.7) + ...
The sum of this series oscillates between 0 and 6.7, never converging unless 6.7 is 0.
In Number Theory
For integer values:
- If 6.7 is even, its additive inverse is also even.
- If 6.7 is odd, its additive inverse is also odd.
- The sum of the digits of 6.7 and its additive inverse may or may not be the same.
Interactive Additive Inverse Calculator
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