1.1 Additive Inverse :
The additive inverse of 1.1 is -1.1.
This means that when we add 1.1 and -1.1, the result is zero:
1.1 + (-1.1) = 0
Additive Inverse of a Decimal Number
For decimal numbers, we simply change the sign of the number:
- Original number: 1.1
- Additive inverse: -1.1
To verify: 1.1 + (-1.1) = 0
Extended Mathematical Exploration of 1.1
Let's explore various mathematical operations and concepts related to 1.1 and its additive inverse -1.1.
Basic Operations and Properties
- Square of 1.1: 1.21
- Cube of 1.1: 1.331
- Square root of |1.1|: 1.0488088481702
- Reciprocal of 1.1: 0.90909090909091
- Double of 1.1: 2.2
- Half of 1.1: 0.55
- Absolute value of 1.1: 1.1
Trigonometric Functions
- Sine of 1.1: 0.89120736006144
- Cosine of 1.1: 0.45359612142558
- Tangent of 1.1: 1.9647596572487
Exponential and Logarithmic Functions
- e^1.1: 3.0041660239464
- Natural log of 1.1: 0.095310179804325
Floor and Ceiling Functions
- Floor of 1.1: 1
- Ceiling of 1.1: 2
Interesting Properties and Relationships
- The sum of 1.1 and its additive inverse (-1.1) is always 0.
- The product of 1.1 and its additive inverse is: -1.21
- The average of 1.1 and its additive inverse is always 0.
- The distance between 1.1 and its additive inverse on a number line is: 2.2
Applications in Algebra
Consider the equation: x + 1.1 = 0
The solution to this equation is x = -1.1, which is the additive inverse of 1.1.
Graphical Representation
On a coordinate plane:
- The point (1.1, 0) is reflected across the y-axis to (-1.1, 0).
- The midpoint between these two points is always (0, 0).
Series Involving 1.1 and Its Additive Inverse
Consider the alternating series: 1.1 + (-1.1) + 1.1 + (-1.1) + ...
The sum of this series oscillates between 0 and 1.1, never converging unless 1.1 is 0.
In Number Theory
For integer values:
- If 1.1 is even, its additive inverse is also even.
- If 1.1 is odd, its additive inverse is also odd.
- The sum of the digits of 1.1 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: