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Chapter 1: Problem 39

Write the given numbers in order from smallest to largest. $$736,662,204,981,399$$

Short Answer

Expert verified
The numbers in order from smallest to largest are 204, 399, 662, 736, 981.

Step by step solution

01

Identify the numbers

The numbers given are 736, 662, 204, 981 and 399.
02

Compare the numbers

By comparing these numbers, it can be seen that 204 is the smallest number and 981 is the largest number.
03

Arrange the numbers

Arranging these numbers from the smallest to the largest we have: 204, 399, 662, 736, 981.

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Key Concepts

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

Comparing Numbers
When it comes to comparing numbers, the essential aim is to determine the relative size of different values. We decide which number is smallest, which is largest, and how the other numbers fit between them. This process involves looking at each number and considering its value based on the digits' position.
  • The first step is to begin with the digit in the highest place value. In our example, this would be the hundreds place.
  • If the numbers have the same hundreds digit, then move to the next lower place value, which is the tens digit, and so on.
Using this method, we can efficiently compare and sort numbers by their magnitude. For example, in our provided list of numbers, we quickly identify 204 as smaller than 399 because the hundreds digit in 204 (2) is smaller than in 399 (3). This way, we compare down the list until we've organized each number by size.
Arranging Numbers
Arranging numbers involves organizing them in a logical sequence based on their magnitudes. It's similar to lining up objects by height. In mathematics, arranging numbers helps in visualizing data better and solving problems that require sequential order. To arrange numbers, follow these steps:
  • Start by determining your criteria, which is usually from smallest to largest.
  • Use the process of comparing numbers, as discussed earlier, to gauge the size.
  • List the numbers in the determined order.
So when given numbers such as 736, 662, 204, 981, and 399, by comparing, you find the correct order. Using arranging techniques, you can form a coherent sequence such as 204, 399, 662, 736, 981.
Mathematical Order
The term "mathematical order" refers to the arrangement of numbers in a sequence so they make logical sense. This order is foundational in mathematics for ensuring consistency and understanding. Mathematical order is crucial for:
  • Following arithmetic operations correctly.
  • Solving equations systematically.
  • Making data more comprehensible.
In various scenarios, such as sequences, series, or even algorithms, maintaining the correct mathematical order is critical. For our set of numbers, recognizing the mathematical order means listing them logically from the smallest value to the largest: 204, 399, 662, 736, 981. Each step follows from proper comparison and arrangement techniques.
Ascending Order
Ascending order is a way of ranking numbers from the least to the greatest. It's a fundamental concept often used in mathematics and daily life, such as when organizing or ranking items. To arrange numbers in ascending order, consider the following method:
  • Start by identifying the smallest number, then the next smallest, and so on until you've listed all numbers.
  • Ensure each number increments in value from the one before it.
In our example, transforming the numbers 736, 662, 204, 981, 399 into ascending order involves first identifying the smallest (204) through to the largest (981), resulting in the ordered sequence: 204, 399, 662, 736, 981.

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