/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 116 Place the proper symbol ( \(>... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 116

Place the proper symbol ( \(>\) or \(<\) ) in the blank: $$ -4.6 \quad \square\quad-4.5 $$

Short Answer

Expert verified
-4.6 < -4.5

Step by step solution

01

Understand the Number Line

Both numbers, -4.6 and -4.5, are negative. On a number line, numbers increase in value as they move to the right and decrease as they move to the left.
02

Comparing the Numbers

Since both numbers are negative, the number with the smaller absolute value is actually greater. The absolute value of -4.6 is 4.6, while the absolute value of -4.5 is 4.5. Since 4.5 is less than 4.6, -4.5 is greater than -4.6.
03

Place the Correct Symbol

Because -4.5 is greater than -4.6, we use the less than symbol (`<`) to show this relationship. The expression becomes: \[-4.6 < -4.5\]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Absolute Value
Absolute value is a mathematical concept that refers to the distance of a number from zero on the number line, without regard to its direction. This means that both negative and positive numbers have the same absolute value if they are the same distance from zero.
For instance:
  • The absolute value of -3 is 3.
  • The absolute value of 3 is also 3.
The absolute value is always a non-negative number. For negative numbers, it reflects the magnitude without the negative sign. In problems involving inequality or locating positions on the number line, understanding absolute values helps determine which numbers are closer or further from zero. This can be particularly useful when comparing numbers, especially negative ones.
Negative Numbers
Negative numbers are numbers less than zero, and they are represented with a minus sign (-). They are the mirror counterpart of positive numbers on the number line.
Here are some key points about negative numbers:
  • They are used to represent values less than zero, like debts or temperatures below freezing.
  • On the number line, they appear to the left of zero.
  • The more negative a number is, the smaller its value. For example, -5 is less than -2.
When dealing with negative numbers, it's helpful to visualize them on the number line, where they give a clearer sense of order and size compared to one another. Remember, when comparing negative numbers, the number with the smaller absolute value is larger.
Comparing Numbers
Comparing numbers, especially negatives, involves understanding their position and magnitude on the number line. When we compare two numbers, we determine which is larger or smaller.
For comparing negative numbers:
  • The number closer to zero is larger. For example, -4.5 is greater than -4.6 because it is closer to zero.
  • Use the concept of absolute value to help decide which is larger. The number with the smaller absolute value is actually larger when both numbers are negative.
  • Symbols such as `>` and `<` show relationships: - `>` means greater than. - `<` means less than.
In our original exercise, although -4.6 seems smaller when looking at its digits, it is actually larger in magnitude (less negative) than a number like -4.5. This is why in the comparison of \(-4.6 \quad < \quad-4.5\). Understanding these comparisons accurately reveals the true relationship between numbers on a number line.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Solve each formula for the specified variable. See Example 5. $$ I=P r t \quad \text { for } t $$

Landscaping. The perimeter of a square flowerbed is 26 yards. Find the length of one side of the flowerbed. Advertising. The perimeter of a triangular banner is 250 inches. If two sides of the banner are each 94.76 in. long, what is the length of the third side?

Perform the operations. See Examples 4 and 5 . $$ \frac{84}{-6} $$

Simplify by combining like terms. See Example 5 . $$1.8 x^{2}-5.1 x^{2}+4.1 x^{2}$$

Translate into mathematical symbols: ten less than twice \(x\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Calculus

Read Explanation

Applied Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.