Select All Numbers That Have An Absolute Value Of 0.Choose All Answers That Apply:A. { -\frac{1}{10}$}$B. 10C. 0D. -0.01
In mathematics, the absolute value of a number is its distance from zero on the number line. It is always non-negative and is denoted by the symbol |x|, where x is the number. When we say that a number has an absolute value of 0, it means that the number is equal to zero.
Understanding Absolute Value
The absolute value of a number x is defined as:
|x| = {x if x ≥ 0
- x if x < 0
In other words, if the number is positive or zero, its absolute value is the number itself. If the number is negative, its absolute value is the positive version of the number.
Selecting Numbers with an Absolute Value of 0
To select numbers with an absolute value of 0, we need to find numbers that are equal to zero. Let's examine the options given:
A. [-\frac{1}{10}]
The absolute value of -\frac{1}{10} is \frac{1}{10}, which is not equal to zero. Therefore, option A is not a correct answer.
B. 10
The absolute value of 10 is 10, which is not equal to zero. Therefore, option B is not a correct answer.
C. 0
The absolute value of 0 is 0, which is equal to zero. Therefore, option C is a correct answer.
D. -0.01
The absolute value of -0.01 is 0.01, which is not equal to zero. Therefore, option D is not a correct answer.
Conclusion
In conclusion, the only number with an absolute value of 0 is 0. Therefore, the correct answer is option C.
Additional Examples
To further illustrate this concept, let's consider a few more examples:
- The absolute value of 5 is 5, which is not equal to zero.
- The absolute value of -5 is 5, which is not equal to zero.
- The absolute value of 0 is 0, which is equal to zero.
- The absolute value of -0.5 is 0.5, which is not equal to zero.
Key Takeaways
- The absolute value of a number is its distance from zero on the number line.
- A number with an absolute value of 0 is equal to zero.
- The only number with an absolute value of 0 is 0.
Common Mistakes
- Many students mistakenly think that the absolute value of a negative number is the negative number itself. However, the absolute value of a negative number is actually the positive version of the number.
- Some students may also think that the absolute value of a fraction is the fraction itself. However, the absolute value of a fraction is the absolute value of the numerator divided by the absolute value of the denominator.
Real-World Applications
Understanding absolute value is crucial in many real-world applications, such as:
- Physics: When calculating distances and velocities, absolute value is used to ensure that the results are always non-negative.
- Engineering: In designing systems and structures, absolute value is used to ensure that the results are always non-negative.
- Finance: In calculating profits and losses, absolute value is used to ensure that the results are always non-negative.
Conclusion
Frequently Asked Questions
In this article, we will answer some of the most frequently asked questions about absolute value.
Q: What is absolute value?
A: Absolute value is a mathematical concept that represents the distance of a number from zero on the number line. It is denoted by the symbol |x|, where x is the number.
Q: How do I calculate the absolute value of a number?
A: To calculate the absolute value of a number, you can follow these steps:
- If the number is positive or zero, its absolute value is the number itself.
- If the number is negative, its absolute value is the positive version of the number.
Q: What is the absolute value of 0?
A: The absolute value of 0 is 0.
Q: What is the absolute value of -5?
A: The absolute value of -5 is 5.
Q: What is the absolute value of 5?
A: The absolute value of 5 is 5.
Q: Can the absolute value of a number be negative?
A: No, the absolute value of a number is always non-negative.
Q: Can the absolute value of a number be zero?
A: Yes, the absolute value of 0 is 0.
Q: How do I use absolute value in real-world applications?
A: Absolute value is used in many real-world applications, such as:
- Physics: When calculating distances and velocities, absolute value is used to ensure that the results are always non-negative.
- Engineering: In designing systems and structures, absolute value is used to ensure that the results are always non-negative.
- Finance: In calculating profits and losses, absolute value is used to ensure that the results are always non-negative.
Q: What are some common mistakes to avoid when working with absolute value?
A: Some common mistakes to avoid when working with absolute value include:
- Thinking that the absolute value of a negative number is the negative number itself.
- Thinking that the absolute value of a fraction is the fraction itself.
- Not considering the absolute value when working with inequalities.
Q: How do I determine if a number is positive or negative?
A: To determine if a number is positive or negative, you can follow these steps:
- If the number is greater than 0, it is positive.
- If the number is less than 0, it is negative.
- If the number is equal to 0, it is neither positive nor negative.
Q: Can I use absolute value to compare two numbers?
A: Yes, you can use absolute value to compare two numbers. For example, if you want to compare the absolute values of 5 and -5, you can say that the absolute value of 5 is greater than the absolute value of -5.
Q: How do I use absolute value in algebraic expressions?
A: To use absolute value in algebraic expressions, you can follow these steps:
- When working with absolute value, you can use the symbol |x| to represent the absolute value of x.
- When simplifying expressions, you can remove the absolute value symbol if the expression inside the absolute value is non-negative.
Conclusion
In conclusion, absolute value is a fundamental concept in mathematics that is used to represent the distance of a number from zero on the number line. By understanding the concept of absolute value and how it is used in real-world applications, you can solve problems and make informed decisions with confidence.