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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

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-1000, r=0.1\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, \ldots\)

You will develop geometric sequences that model the population growth for California and Texas, the two most populated U.S. states. The table shows the population of Texas for 2000 and 2010 , with estimates given by the U.S. Census Bureau for 2001 through \(2009 .\) $$ \begin{aligned} &\begin{array}{|l|c|c|c|c|c|c|} \hline \text { Year } & \mathbf{2 0 0 0} & \mathbf{2 0 0 1} & \mathbf{2 0 0 2} & \mathbf{2 0 0 3} & \mathbf{2 0 0 4} & \mathbf{2 0 0 5} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 20.85 & 21.27 & 21.70 & 22.13 & 22.57 & 23.02 \\ \hline \end{array}\\\ &\begin{array}{|l|c|c|c|c|c|} \hline \text { Year } & \mathbf{2 0 0 6} & \mathbf{2 0 0 7} & \mathbf{2 0 0 8} & \mathbf{2 0 0 9} & \mathbf{2 0 1 0} \\ \hline \begin{array}{l} \text { Population } \\ \text { in millions } \end{array} & 23.48 & 23.95 & 24.43 & 24.92 & 25.15 \\ \hline \end{array} \end{aligned} $$ a. Divide the population for each year by the population in the preceding year. Round to two decimal places and show that Texas has a population increase that is approximately geometric. b. Write the general term of the geometric sequence modeling Texas's population, in millions, \(n\) years after \(1999 .\) c. Use your model from part (b) to project Texas's population, in millions, for the year 2020 . Round to two decimal places.

Write a formula for the general term (the nth term) of each geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(3,15,75,375, \ldots\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-\frac{1}{16}, r=-4\)
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