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Chapter 2: Problem 44

Write the numbers in increasing order. \(4.6,0.7,-4,-1.8,3,-0.6\)

Short Answer

Expert verified
-4, -1.8, -0.6, 0.7, 3, 4.6

Step by step solution

01

Identify the numerical value of each number

In our list we have both positive and negative numbers. Negative numbers are always less than positive numbers. So in our case, -4 and -1.8 are our lowest numbers.
02

Arrange all numbers in increasing order

We start with our lowest numbers, then move on to the next lowest number, and continue this process until we've ordered all of our numbers. From lowest to highest, the correct order should be: -4, -1.8, -0.6, 0.7, 3, 4.6.
03

Write down the final list

The final list in increasing order should be written down as: \( -4, -1.8, -0.6, 0.7, 3, 4.6 \)

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Key Concepts

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

Understanding Positive and Negative Numbers
Positive and negative numbers are fundamental parts of mathematics and they represent different concepts. Positive numbers are greater than zero and often signify quantities we can count or measure, like 3 apples or $4.50. In contrast, negative numbers are less than zero and usually indicate a deficiency or a loss, such as having a debt of -4 dollars or being 1.8 meters below sea level.

When comparing these numbers, remember:
  • Positive numbers are always greater than negative numbers.
  • The larger the positive number, the greater its value.
  • The smaller the negative number (meaning closer to zero), the greater its value within the negatives.
In our given set of numbers, -4 is the smallest because it is the most negative, while 4.6 is the largest because it is the most positive.
How to Use Numerical Order
Numerical order refers to arranging numbers from smallest to largest (or vice versa). This is common in math to help organize data and identify relationships between numbers. When ordering numbers, you simply start with the smallest (or largest if descending) and move towards the other extreme.

In our list, we must first separate positive from negative, remembering that all negative numbers will precede positives in an increasing order. After identifying whether a number is positive or negative, we further compare them:
  • Among negative numbers, -4 precedes -1.8 because -4 is smaller.
  • Among positive numbers, 0.7 comes before 3, followed by 4.6 as the largest.
Understanding these basic principles of numerical order allows us to confidently arrange any set of numbers.
Arranging Numbers Step-by-Step
Arranging numbers effectively involves a systematic approach. Let's apply it to our set: -4, -1.8, -0.6, 0.7, 3, and 4.6. First, gather all the numbers you need to arrange. Look at signs to determine the initial separation into negatives and positives.

Here鈥檚 a helpful process:
  • Step 1: List all negative numbers and arrange them starting with the smallest. For our set, this is -4, -1.8, then -0.6.
  • Step 2: List all positive numbers and arrange starting from the smallest. Here, it's 0.7, then 3, and finally 4.6.
  • Step 3: Combine these sequences, placing all negative numbers before any positive numbers to achieve the increasing order.
Following this method ensures accuracy and simplicity in ordering numbers, making it an essential skill for organizing numerical data correctly.

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