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Chapter 1: Problem 22

Find each absolute value. $$ |-5.3(10)| $$

Short Answer

Expert verified
|-5.3(10)| = 53

Step by step solution

01

Understand Absolute Value

The absolute value of a number represents its distance from zero on the number line, regardless of direction. Mathematically, it is always non-negative. For any real number x, \(|x| = x\) if x is positive or zero, and \(|x| = -x\) if x is negative.
02

Simplify the Expression Inside the Absolute Value

First, simplify the expression inside the absolute value. Calculate \(-5.3 \cdot 10\). This multiplication gives us: \-5.3 \cdot 10 = -53.
03

Apply the Absolute Value

Now, apply the absolute value to -53. According to the absolute value definition, \(|-53| = 53\) because the absolute value of a negative number is its positive counterpart.

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Key Concepts

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

absolute value
The absolute value of a number shows how far away the number is from zero on the number line.
It doesn't matter if the number is positive or negative.
We denote the absolute value using vertical bars, like this: \(|x|\).
For example, \(|-5|\) and \(|5|\) both equal 5, because both -5 and 5 are 5 units away from zero.
The absolute value turns any negative number positive, but positive numbers and zero stay the same.
To summarize, the absolute value of a number is always non-negative.
number line
A number line is a visual tool to show the position of numbers in a straight row.
Zero is typically in the middle, with positive numbers to the right and negative numbers to the left.
Each point on the number line represents a real number and the distance between each point is consistent.
For example, moving from -2 to 2 on the number line, you pass 0, showing that -2 and 2 are equidistant from zero, just in opposite directions.
When talking about absolute value, the number line helps to visualize how far a number is from zero, whether it's negative or positive.
multiplication of decimals
Multiplying decimals can be tricky, but there's an easy method.
First, ignore the decimal points and simply multiply the numbers as if they were whole numbers.
Then, count the total number of decimal places in both of the original numbers.
Finally, place the decimal point in the answer by counting from the right, ensuring it has the same number of decimal places.
For example, for the expression \(-5.3 \cdot 10\), we multiply 5.3 by 10, ignoring the negative sign for now. This gives us 53.
Since there is one decimal place in 5.3, our multiplication result of 53 will have one decimal place: -53.0.
The negative sign is added last: -53.

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Most popular questions from this chapter

Describe in your own words a method for determining the sign of the sum of a positive number and a negative number.

Write an equivalent expression using an associative law. $$ -7(a b) $$

Calculate using the rules for order of operations. If an expression is undefined, state this. $$ 9-\left(8-3 \cdot 2^{3}\right) $$

Which numbers in the list provided are (a) whole numbers? (b) integers? (c) rational numbers? (d) irrational numbers? (e) real numbers?. $$ -17,-0.01,0, \frac{5}{4}, 8, \sqrt{77} $$

Translate to an algebraic expression. The product of the difference of two numbers and their sum
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