2.2 Arrange The Following Numbers In Ascending Order. 258 121:865 153:721 122 :903 546:865 199: 831001 2.3 Use Or = To Compare The Numbers Below: 2.3.1. 983 815 938 815 (1) 2.3.2. 505 082 500 000 + 8 Tens + 5 Ten Thousands + 2 (1) 2.3.3. 500+ 60 000+

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Introduction

In mathematics, arranging numbers in ascending order and comparing values are essential skills that help us understand the relationships between numbers. In this article, we will explore how to arrange numbers in ascending order and compare values using various mathematical operations.

Arranging Numbers in Ascending Order

2.2 Arrange the following numbers in ascending order.

To arrange numbers in ascending order, we need to compare each number with the others and place them in order from smallest to largest.

  • 258
  • 121:865
  • 153:721
  • 122:903
  • 546:865
  • 199:831001

Let's break down each number and compare them:

  • 258: This is a simple number that can be compared with others easily.
  • 121:865: To compare this number, we need to convert it to a decimal number. 121:865 can be written as 121 + 865/100 = 121 + 8.65 = 129.65.
  • 153:721: Similarly, we can convert this number to a decimal number. 153:721 can be written as 153 + 721/100 = 153 + 7.21 = 160.21.
  • 122:903: Converting this number to a decimal, we get 122 + 903/100 = 122 + 9.03 = 131.03.
  • 546:865: Converting this number to a decimal, we get 546 + 865/100 = 546 + 8.65 = 554.65.
  • 199:831001: This is a large number, but we can still compare it with others. Converting this number to a decimal, we get 199 + 831001/1000 = 199 + 831 = 1030.

Now that we have converted all the numbers to decimals, we can arrange them in ascending order:

  1. 258
  2. 129.65 (121:865)
  3. 131.03 (122:903)
  4. 160.21 (153:721)
  5. 554.65 (546:865)
  6. 1030 (199:831001)

2.3 Use or = to compare the numbers below:

2.3.1

  • 983
  • 815
  • 938
  • 815 (1)

To compare these numbers, we can simply arrange them in ascending order:

  1. 815
  2. 815 (1)
  3. 983
  4. 938

Since 815 and 815 (1) are equal, we can say that 815 = 815 (1).

2.3.2

  • 505
  • 082
  • 500 000
    • 8 tens
    • 5 ten thousands
    • 2

To compare these numbers, we need to evaluate the expression:

500 000 + 8 tens + 5 ten thousands + 2

First, let's convert the numbers to a common unit:

  • 500 000 = 500 000
  • 8 tens = 80
  • 5 ten thousands = 50 000
    • 2 = 2

Now, let's add the numbers:

500 000 + 80 = 500 080 500 080 + 50 000 = 550 080 550 080 + 2 = 550 082

So, the expression evaluates to 550 082.

Now, let's compare the numbers:

  • 505
  • 082
  • 550 082

Since 082 is equal to 550 082, we can say that 082 = 550 082.

2.3.3

  • 500
    • 60 000

To compare these numbers, we need to evaluate the expression:

500 + 60 000

First, let's add the numbers:

500 + 60 000 = 60 500

Now, let's compare the numbers:

  • 500
  • 60 500

Since 500 is less than 60 500, we can say that 500 < 60 500.

Conclusion

Q: What is the purpose of arranging numbers in ascending order?

A: Arranging numbers in ascending order helps us understand the relationships between numbers and makes it easier to compare and analyze data.

Q: How do I arrange numbers in ascending order?

A: To arrange numbers in ascending order, you need to compare each number with the others and place them in order from smallest to largest. You can convert numbers to decimals to make comparisons easier.

Q: What is the difference between arranging numbers in ascending order and comparing values?

A: Arranging numbers in ascending order involves placing numbers in order from smallest to largest, while comparing values involves evaluating expressions and determining whether they are equal, greater than, or less than each other.

Q: How do I compare values using equal to (=) and less than (<) symbols?

A: To compare values using equal to (=) and less than (<) symbols, you need to evaluate expressions and determine whether they are equal, greater than, or less than each other. For example, if you have two numbers, 5 and 7, you can say that 5 < 7 because 5 is less than 7.

Q: What is the importance of comparing values in mathematics?

A: Comparing values is an essential skill in mathematics that helps us understand the relationships between numbers and make informed decisions. It is used in various mathematical operations, such as addition, subtraction, multiplication, and division.

Q: How do I evaluate expressions with multiple numbers and operations?

A: To evaluate expressions with multiple numbers and operations, you need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: What are some common mistakes to avoid when comparing values?

A: Some common mistakes to avoid when comparing values include:

  • Not following the order of operations (PEMDAS)
  • Not converting numbers to decimals when necessary
  • Not evaluating expressions carefully
  • Not checking for errors in calculations

Q: How can I practice comparing values and arranging numbers in ascending order?

A: You can practice comparing values and arranging numbers in ascending order by:

  • Solving mathematical problems and exercises
  • Practicing with online resources and worksheets
  • Working with a tutor or teacher to review and practice concepts
  • Participating in math competitions and challenges

Conclusion

In this article, we answered frequently asked questions on arranging numbers in ascending order and comparing values. We covered topics such as the purpose of arranging numbers in ascending order, how to arrange numbers in ascending order, and the importance of comparing values in mathematics. By following these tips and practicing regularly, you can develop your mathematical skills and become more confident in solving mathematical problems.