Evaluate The Following Absolute Value: ∣ − 7.285 ∣ |-7.285| ∣ − 7.285∣

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Introduction

In mathematics, the absolute value of a number is its distance from zero on the number line. It is a measure of the magnitude or size of a number, without considering its direction or sign. The absolute value of a number is always non-negative, and it is denoted by two vertical lines around the number, such as $|x|$. In this article, we will evaluate the absolute value of the decimal number $-7.285$.

Understanding Absolute Value

The absolute value of a number is defined as its distance from zero on the number line. For example, the absolute value of $5$ is $5$, because it is $5$ units away from zero on the number line. Similarly, the absolute value of $-5$ is also $5$, because it is also $5$ units away from zero on the number line. This means that the absolute value of a number is always non-negative, and it is the same as the number if the number is non-negative, and it is the negative of the number if the number is negative.

Evaluating the Absolute Value of $-7.285$

To evaluate the absolute value of $-7.285$, we need to find its distance from zero on the number line. Since $-7.285$ is a negative number, its absolute value will be its positive counterpart. Therefore, the absolute value of $-7.285$ is $7.285$.

Properties of Absolute Value

The absolute value of a number has several important properties that are useful in mathematics. Some of these properties are:

• Non-Negativity: The absolute value of a number is always non-negative.
• Identity: The absolute value of a non-negative number is the number itself.
• Symmetry: The absolute value of a negative number is the negative of the number.
• Triangle Inequality: The absolute value of the sum of two numbers is less than or equal to the sum of their absolute values.

Examples of Evaluating Absolute Value

Here are some examples of evaluating the absolute value of decimal numbers:

• $|3.5| = 3.5$
• $|-2.7| = 2.7$
• $|0.5| = 0.5$
• $|-0.5| = 0.5$

Applications of Absolute Value

The absolute value of a number has many applications in mathematics and other fields. Some of these applications are:

• Distance: The absolute value of a number can be used to measure the distance between two points on a number line.
• Magnitude: The absolute value of a number can be used to measure the magnitude or size of a number.
• Error Analysis: The absolute value of a number can be used to analyze errors in measurement or calculation.
• Signal Processing: The absolute value of a number can be used in signal processing to remove noise or to detect patterns in data.

Conclusion

In conclusion, the absolute value of a decimal number is its distance from zero on the number line. It is a measure of the magnitude or size of a number, without considering its direction or sign. The absolute value of a number is always non-negative, and it is denoted by two vertical lines around the number. In this article, we evaluated the absolute value of the decimal number $-7.285$ and discussed its properties and applications.

Frequently Asked Questions

• What is the absolute value of a negative number? The absolute value of a negative number is its positive counterpart.
• What is the absolute value of a non-negative number? The absolute value of a non-negative number is the number itself.
• What is the absolute value of zero? The absolute value of zero is zero.

References

• Khan Academy: Absolute Value
• Math Is Fun: Absolute Value
• Wikipedia: Absolute Value
  

Introduction

In our previous article, we discussed the concept of absolute value and how it is used to measure the magnitude or size of a number. In this article, we will answer some frequently asked questions about absolute value, covering topics such as the definition of absolute value, properties of absolute value, and examples of evaluating absolute value.

Q&A: Absolute Value

Q1: What is the definition of absolute value?

A1: The absolute value of a number is its distance from zero on the number line. It is a measure of the magnitude or size of a number, without considering its direction or sign.

Q2: What is the absolute value of a negative number?

A2: The absolute value of a negative number is its positive counterpart. For example, the absolute value of $-5$ is $5$.

Q3: What is the absolute value of a non-negative number?

A3: The absolute value of a non-negative number is the number itself. For example, the absolute value of $5$ is $5$.

Q4: What is the absolute value of zero?

A4: The absolute value of zero is zero. This is because zero is neither positive nor negative, and its distance from zero on the number line is zero.

Q5: How do I evaluate the absolute value of a decimal number?

A5: To evaluate the absolute value of a decimal number, you need to find its distance from zero on the number line. This can be done by simply removing the negative sign, if present, and keeping the positive sign.

Q6: What are some properties of absolute value?

A6: Some properties of absolute value include:

• Non-Negativity: The absolute value of a number is always non-negative.
• Identity: The absolute value of a non-negative number is the number itself.
• Symmetry: The absolute value of a negative number is the negative of the number.
• Triangle Inequality: The absolute value of the sum of two numbers is less than or equal to the sum of their absolute values.

Q7: How do I use absolute value in real-life situations?

A7: Absolute value is used in many real-life situations, such as:

• Distance: The absolute value of a number can be used to measure the distance between two points on a number line.
• Magnitude: The absolute value of a number can be used to measure the magnitude or size of a number.
• Error Analysis: The absolute value of a number can be used to analyze errors in measurement or calculation.
• Signal Processing: The absolute value of a number can be used in signal processing to remove noise or to detect patterns in data.

Q8: Can I use absolute value with fractions?

A8: Yes, you can use absolute value with fractions. The absolute value of a fraction is the absolute value of its numerator divided by the absolute value of its denominator.

Q9: Can I use absolute value with negative numbers in the denominator?

A9: Yes, you can use absolute value with negative numbers in the denominator. The absolute value of a fraction with a negative number in the denominator is the absolute value of its numerator divided by the absolute value of its denominator.

Q10: How do I evaluate the absolute value of a complex number?

A10: To evaluate the absolute value of a complex number, you need to use the formula $|a+bi| = \sqrt{a^2 + b^2}$, where $a$ and $b$ are the real and imaginary parts of the complex number, respectively.

Conclusion

In conclusion, absolute value is a fundamental concept in mathematics that is used to measure the magnitude or size of a number. It has many properties and applications, and is used in many real-life situations. We hope that this Q&A article has helped to clarify any questions you may have had about absolute value.

Frequently Asked Questions

• What is the absolute value of a negative number? The absolute value of a negative number is its positive counterpart.
• What is the absolute value of a non-negative number? The absolute value of a non-negative number is the number itself.
• What is the absolute value of zero? The absolute value of zero is zero.

References

• Khan Academy: Absolute Value
• Math Is Fun: Absolute Value
• Wikipedia: Absolute Value