Mastering Terminating and Repeating Decimals

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Mastering Terminating and Repeating Decimals

Table of Contents

  1. Introduction
  2. Terminating Decimals
  3. Long Division Method
  4. Example 1: Converting 2/5 into a Decimal
  5. Example 2: Converting 1/3 into a Decimal
  6. Example 3: Converting 2 and 1737/100 into a Decimal
  7. Example 4: Converting 8/3 into a Decimal
  8. Example 5: Converting 11/6 into a Decimal
  9. Example 6: Converting 16/15 into a Decimal
  10. Conclusion

Converting Fractions into Decimals: A Step-by-Step Guide

Fractions and decimals are two different forms of representing numbers. Sometimes, it becomes necessary to convert fractions into decimals for various mathematical operations or better understanding. In this article, we will explore the concept of converting fractions into decimals and learn the step-by-step process involved in this conversion.

1. Introduction

Understanding the conversion of fractions into decimals is crucial in mathematics. By converting a fraction into a decimal, we can express the fraction in a more versatile form that is helpful in calculations, comparisons, and real-life applications. The two types of decimals we will discuss in this article are terminating decimals and repeating decimals. Let's Delve deeper into each Type and explore the methods used to convert fractions into decimals.

2. Terminating Decimals

A terminating decimal is a decimal that has a definite number of digits after the decimal point. In other words, it does not go on infinitely. Terminating decimals can be easily represented as fractions where the denominator is a power of 10 (such as 10, 100, 1000, etc.). These decimals can be converted into fractions in a straightforward manner. However, not all fractions result in terminating decimals.

3. Long Division Method

To convert a fraction into a decimal, we will use the long division method. This method involves dividing the numerator by the denominator to obtain the decimal representation of the fraction. Let's take a look at some examples to understand the process better.

4. Example 1: Converting 2/5 into a Decimal

Let's convert the fraction 2/5 into a decimal using the long division method.

Step 1: Set up the long division with the denominator (5) on the outside and the numerator (2) on the inside. Place a decimal point above the division line.

Step 2: Divide:

                   0.4
                ________
        5  |   2
           -  0
             ------
          (Repeat if necessary)

Since the division results in a remainder of 0, the decimal representation of the fraction 2/5 is 0.4. It is a terminating decimal.

5. Example 2: Converting 1/3 into a Decimal

Let's convert the fraction 1/3 into a decimal using the long division method.

Step 1: Set up the long division with the denominator (3) on the outside and the numerator (1) on the inside. Place a decimal point above the division line.

Step 2: Divide:

                   0.3̅
                ________
        3  |   1
           -  0
             ------
          (Repeat if necessary)

Since the division results in a repeating pattern of digits (the digit 3 in this case), the decimal representation of the fraction 1/3 is 0.3̅, where the line above the digit 3 indicates the repetition. It is a repeating decimal.

6. Example 3: Converting 2 and 1737/100 into a Decimal

Let's convert the mixed number 2 and 1737/100 into a decimal using the long division method.

Step 1: Focus on the fraction part (1737/100). Set up the long division with the denominator (100) on the outside and the numerator (1737) on the inside. Place a decimal point above the division line.

Step 2: Divide:

                  2.1737̅
               ___________
       100  |   1737
           -  1700
             ------
            (Repeat if necessary)

Since the division results in a repeating decimal (1737̅), the decimal representation of the mixed number 2 and 1737/100 is 2.1737̅, where the line above the digits 1737 indicates the repetition.

7. Example 4: Converting 8/3 into a Decimal

Let's convert the fraction 8/3 into a decimal using the long division method.

Step 1: Set up the long division with the denominator (3) on the outside and the numerator (8) on the inside. Place a decimal point above the division line.

Step 2: Divide:

                   2.6666̅
                ___________
        3  |   8
           -  6
             ------
          (Repeat if necessary)

Since the division results in a repeating decimal (6̅), the decimal representation of the fraction 8/3 is 2.6666̅, where the line above the digit 6 indicates the repetition.

8. Example 5: Converting 11/6 into a Decimal

Let's convert the fraction 11/6 into a decimal using the long division method.

Step 1: Set up the long division with the denominator (6) on the outside and the numerator (11) on the inside. Place a decimal point above the division line.

Step 2: Divide:

                   1.8̅3
                ________
        6  |   11
           -  6
             ------
          (Repeat if necessary)

Since the division results in a repeating decimal (8̅3), the decimal representation of the fraction 11/6 is 1.8̅3, where the line above the digits 8 and 3 indicates the repetition.

9. Example 6: Converting 16/15 into a Decimal

Let's convert the fraction 16/15 into a decimal using the long division method.

Step 1: Set up the long division with the denominator (15) on the outside and the numerator (16) on the inside. Place a decimal point above the division line.

Step 2: Divide:

                   1.0̅6
                ________
        15  |   16
           -  15
             ------
          (Repeat if necessary)

Since the division results in a repeating decimal (0̅6), the decimal representation of the fraction 16/15 is 1.0̅6, where the line above the digit 0 and 6 indicates the repetition.

10. Conclusion

Converting fractions into decimals is a valuable skill in mathematics. By using the long division method, we can convert fractions into both terminating and repeating decimals. Terminating decimals have a finite number of digits after the decimal point, while repeating decimals have a repeating pattern of digits. Understanding this conversion process helps in various mathematical calculations and real-world applications, enhancing our mathematical skills.

Highlights:

  • Converting fractions into decimals is a crucial skill in mathematics.
  • Terminating decimals have a definite number of digits after the decimal point.
  • Repeating decimals have a repeating pattern of digits.
  • The long division method is used to convert fractions into decimals.
  • Terminating decimals can be easily converted into fractions.
  • Repeating decimals require a line above the repeating digit(s) to indicate repetition.
  • Knowing the conversion of fractions into decimals enhances mathematical calculations and real-world applications.

Frequently Asked Questions (FAQs)

Q1: What is the purpose of converting fractions into decimals? Converting fractions into decimals allows us to express fractions in a more versatile form that is useful for calculations, comparisons, and real-life applications.

Q2: What are the two types of decimals discussed in the article? The two types of decimals discussed in the article are terminating decimals and repeating decimals.

Q3: How can I convert a fraction into a terminating decimal? To convert a fraction into a terminating decimal, use the long division method and check if the division results in a remainder of 0.

Q4: How can I convert a fraction into a repeating decimal? To convert a fraction into a repeating decimal, use the long division method and look for a repeating pattern of digits after the decimal point, indicating a repeating decimal.

Q5: Why is it important to know the conversion of fractions into decimals? Knowing how to convert fractions into decimals expands our mathematical skills and enables us to perform various calculations and understand real-life applications more effectively.

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