Understanding 1 and 1/5 as a Decimal: A Comprehensive Guide

Introduction

In the realm of mathematics, fractions play a vital role in representing parts of a whole. However, understanding fractions can be daunting, especially when converting them to their decimal equivalents. One such fraction that often poses a challenge is 1 and 1/5. This article delves into the conversion of 1 and 1/5 to a decimal, exploring various strategies and providing insightful examples.

Step-by-Step Conversion

To convert 1 and 1/5 to a decimal, we can follow these steps:

1. Express the fraction as an improper fraction: Multiply the whole number (1) by the denominator (5) and add the numerator (1). 1 * 5 + 1 = 6
2. Place the result over the denominator: 6/5
3. Perform long division: Divide the numerator (6) by the denominator (5) to obtain the decimal equivalent.

     1.2
5 ) 6.0
    5  
    ---   
     10   
     10  
    ---   
      0

Therefore, 1 and 1/5 as a decimal is 1.2.

Effective Strategies

Converting fractions to decimals can be simplified using various strategies:

• Long Division: As demonstrated earlier, long division provides a straightforward method for converting fractions to decimals.
• Decimal Place Conversion: Multiply the fraction by a power of 10 to move the decimal point to a desired place. For example, to convert 1 and 1/5 to a decimal with two decimal places, multiply by 100: (1 and 1/5) * 100 = 120.00
• Unit Conversion: Convert the fraction to a decimal by dividing the numerator by the denominator. For instance, 1 and 1/5 can be expressed as 1.2 by dividing 1 by 5.

Common Mistakes to Avoid

When converting fractions to decimals, it's important to avoid common pitfalls:

• Rounding Errors: Avoid rounding the decimal result prematurely. Instead, perform the division until the desired accuracy is achieved.
• Improper Fraction Confusion: Ensure that the fraction is properly converted to an improper fraction before performing long division.

Applications of 1.2 as a Decimal

The decimal equivalent of 1 and 1/5 has numerous applications in different fields:

• Measurements: In measurements, 1.2 is commonly used to represent 120% of a given value.
• Percentages: In finance and statistics, 1.2 is equivalent to 120% or 120 out of 100.
• Decimal Representation: In computing and mathematics, 1.2 is the decimal representation of the fraction 6/5.

Table 1: Conversion Techniques for 1 and 1/5 to Decimal

Table 2: Applications of 1.2 as a Decimal

Table 3: Common Mistakes in Converting 1 and 1/5 to Decimal

FAQs

1. How is 1 and 1/5 expressed as a decimal using long division?
   - 6/5 = 1.2

   

2. What is 1 and 1/5 multiplied by 100 in decimal form?
   - 120.00

3. Is 1.2 the same as 120%?
   - Yes, 1.2 is equivalent to 120%.

4. What is the proper way to convert 1 and 1/5 to an improper fraction?
   - 1 * 5 + 1 = 6/5

5. How many decimal places should be used when converting 1 and 1/5 to a decimal?
   - The number of decimal places depends on the desired accuracy.

6. What is the best strategy for converting fractions to decimals?
   - The best strategy is to use the method that is most comfortable for the individual, such as long division or unit conversion.

7. Is it possible to find the decimal equivalent of a fraction without using a calculator?
   - Yes, it is possible using methods like long division or unit conversion.

8. What are the common applications of 1.2 as a decimal?
   - Measurements, percentages, and decimal representation.