/*! 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 64 Insert either \(a<\) or \(a&g... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 1: Problem 64

Insert either \(a<\) or \(a>\) symbol to make a true statement. $$ -6.07 \quad-\frac{17}{6} $$

Short Answer

Expert verified
The correct symbol is <, so \\(-6.07 < -\frac{17}{6}\\).

Step by step solution

01

Convert fractions to decimals

To compare the two numbers given, it's helpful to convert the fraction to a decimal. The fraction \(-\frac{17}{6}\) can be converted by dividing -17 by 6. \(-\frac{17}{6} = -2.8333...\) (repeating).
02

Compare the decimal numbers

Now compare \(-6.07\) with \(-2.8333...\). A number is smaller if it is more negative. Therefore, \(-6.07\) is less than \(-2.8333...\), since \(-6.07\) is further left on the number line.
03

Insert the correct symbol

Since \(-6.07\) is less than \(-2.8333...\), we use the symbol \(<\) which stands for 'less than'. Therefore, the correct statement is: \(-6.07 < -\frac{17}{6}\).

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.

Comparing Decimals
When comparing decimals, the goal is to determine which of the two numbers is larger or smaller. This doesn't just apply to positive numbers; understanding negative decimals is equally important.
Steps for Comparing Decimals:
  • Align the numbers by their decimal points to ensure an accurate comparison.
  • Start comparing from the leftmost digit. For negative numbers, remember that a number is considered smaller the more negative it is.
  • If the integer part (whole number part) is the same, compare the decimal parts digit by digit.

Consider the numbers \( -6.07 \) and \( -2.8333.... \). With both numbers being negative, \( -6.07 \) is more negative than \( -2.8333... \). Therefore, it is smaller.
Converting Fractions to Decimals
Fractions can often be perplexing, but converting them to decimals can make comparison and other operations more straightforward. The conversion involves division, which turns a fraction into a decimal format.
Steps to Convert Fractions to Decimals:
  • Take the numerator (the top number) and divide it by the denominator (the bottom number).
  • Perform the division to as many decimal places as needed, especially if the decimal is repeating or terminating.
  • If the decimal repeats, note it with a line or ellipsis after the last repeating digit.

For instance, converting the fraction \( -\frac{17}{6} \) is done by dividing -17 by 6. The result \( -2.8333... \) is a repeating decimal which makes it easy to compare with other decimals.
Number Line
A number line is a visual aid that can help effectively compare numbers, even with decimals or fractions. It horizontally represents numbers, allowing you to see which numbers are smaller or larger based on their position from left to right.
Using Number Lines:
  • The left side of the number line indicates smaller numbers or more negative numbers.
  • The right side represents larger numbers or more positive numbers.
  • When positioning decimals, it helps to think about their value in comparison to familiar reference points like 0, -1, 1, etc.

In our example, \( -6.07 \) is placed further left on the number line compared to \( -2.8333... \), visually confirming that it is indeed the smaller number. Using a number line can simplify concepts that might seem abstract at first.

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

a. \(6 a+6 a+6 a\) b. \(6 a+6 b+6 c\)

What does it mean to solve an equation?

Explain how the distributive property can be used to evaluate the expression \(52.713(21)+52.713(79)\) mentally.

Solve each equation. $$ \frac{t-1}{3}=\frac{t+2}{6}+2 $$

A wholesaler of premium organic planting mix notices that the retail garden centers are not buying her product because of its high price of \(\$ 1.57\) per cubic foot. She decides to mix sawdust with the planting mix to lower the price per cubic foot. If the wholesaler can buy the sawdust for \(\$ 0.10\) per cubic foot, how many cubic feet of each must be mixed to have \(6,000\) cubic feet of planting mix that could be sold to retailers for \(\$ 1.08\) per cubic foot?
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Statistics

Read Explanation

Mechanics Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

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.