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Chapter 5: Problem 18

Find the absolute value. \(|-1,000,000|\)

Short Answer

Expert verified
The absolute value of |-1,000,000| is 1,000,000.

Step by step solution

01

Identify the number

The number given is -1,000,000.
02

Apply the Absolute Value Operation

With |-1,000,000|, the absolute value operation means to get the non-negative value of the number. Here, the number is negative so we need to convert it into its positive equivalent.
03

Obtain the Absolute Value

The absolute value of |-1,000,000| is 1,000,000, as the negative sign is removed.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mathematical Operations
Mathematical operations are the foundation of algebra and arithmetic, providing a systematic way to perform calculations. Common operations include addition, subtraction, multiplication, and division.

Each operation has specific rules governing how it is executed and interacts with numbers, whether they are whole numbers, fractions, decimals, or negative numbers. Understanding these operations and their properties is crucial for solving a wide range of mathematical problems.
Non-negative Numbers
Non-negative numbers are all numbers that are not negative, including zero and positive numbers. This category includes whole numbers starting from zero (0, 1, 2, 3, ...) and also encompasses decimals and fractions that are greater than or equal to zero.

Understanding Non-Negative Numbers:

Non-negative numbers are represented on the number line to the right of zero. They are crucial in real-world contexts where negative values are not possible, such as counting items or measuring lengths.
Absolute Value Operation
The absolute value operation is a mathematical function that transforms a number into a non-negative value, regardless of its original sign. It is defined by two vertical bars, like this: \( |x| \).

Applying Absolute Value:

To calculate the absolute value of a number, you take the positive distance of the number from zero. For example, both \( |-3| \) and \( |3| \) equal 3. The absolute value of any negative number will be the number without its negative sign, signifying the distance from zero without regard to direction.
Number Properties
Number properties are rules that describe the behaviors of numbers in various mathematical scenarios. They include the commutative, associative, distributive properties, as well as properties of zero and one.

Absolute Value and Number Properties:

When working with absolute values, one important property to remember is that the absolute value of a number is always non-negative. This property is essential when solving equations and inequalities that involve absolute values, ensuring that solutions are within the realm of real numbers.

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Most popular questions from this chapter

Express each rational number as a decimal. \(\frac{3}{5}\)

Explain the power rule for exponents. Use \(\left(3^{2}\right)^{4}\) in your explanation.

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=3, r=-2\)

Explain how to convert from a mixed number to an improper fraction. Use \(7 \frac{2}{3}\) as an example.

Use the zero and negative exponent rules to simplify each expression. \(3^{-2}\)
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