87 1 2 As A Decimal

87 1/2 as a Decimal: A Comprehensive Guide

Converting fractions to decimals is a fundamental skill in mathematics with widespread applications in various fields. This comprehensive guide delves into the conversion of the mixed number 87 1/2 into its decimal equivalent, exploring different methods and highlighting the importance of understanding this conversion process. We'll also touch upon the practical uses of this conversion and offer further examples to solidify your understanding.

Understanding Mixed Numbers and Decimals

Before diving into the conversion, let's briefly review the concepts of mixed numbers and decimals.

A mixed number combines a whole number and a fraction. In our case, 87 1/2 represents 87 whole units and one-half of a unit.

A decimal is a number expressed in the base-10 numeral system, using a decimal point to separate the whole number part from the fractional part. For example, 12.5 represents twelve and five-tenths.

Converting a mixed number to a decimal involves expressing the fractional part as a decimal and then combining it with the whole number part.

Method 1: Converting the Fraction to a Decimal

The most straightforward method involves converting the fractional part (1/2) to a decimal and then adding it to the whole number (87).

To convert 1/2 to a decimal, we perform the division: 1 ÷ 2 = 0.5

Therefore, 87 1/2 as a decimal is 87 + 0.5 = 87.5

Understanding the Division Process

The division 1 ÷ 2 represents how many times 2 goes into 1. Since 2 is larger than 1, the result is a decimal less than 1. To perform the long division:

1. Add a decimal point and a zero to the 1, making it 1.0.
2. Divide 10 by 2, which equals 5.
3. Therefore, 1/2 = 0.5

Method 2: Converting to an Improper Fraction

An alternative approach involves converting the mixed number into an improper fraction first, and then converting the improper fraction to a decimal.

To convert 87 1/2 to an improper fraction:

1. Multiply the whole number (87) by the denominator of the fraction (2): 87 * 2 = 174
2. Add the numerator of the fraction (1) to the result: 174 + 1 = 175
3. Keep the same denominator (2): The improper fraction is 175/2

Now, convert the improper fraction 175/2 to a decimal by performing the division: 175 ÷ 2 = 87.5

Long Division for Improper Fractions

The long division of 175 ÷ 2 involves:

1. Dividing 17 by 2, which gives 8 with a remainder of 1.
2. Bringing down the 5 to make 15.
3. Dividing 15 by 2, which gives 7 with a remainder of 1.
4. Adding a decimal point and a zero to the remainder 1, making it 10.
5. Dividing 10 by 2, which gives 5.
6. Therefore, 175/2 = 87.5

Practical Applications of Decimal Conversion

The conversion of fractions to decimals is crucial in many real-world applications:

• Finance: Calculating interest rates, discounts, and profit margins often involves working with decimals.
• Engineering: Precise measurements and calculations in engineering projects require decimal representation.
• Science: Scientific data and measurements are often expressed in decimal form.
• Everyday Life: Many everyday calculations, such as splitting bills or calculating tips, use decimal numbers.

Further Examples

Let's practice converting more mixed numbers to decimals using the methods described above:

Example 1: 25 3/4

• Method 1: 3/4 = 0.75; 25 + 0.75 = 25.75
• Method 2: (25 * 4 + 3)/4 = 103/4; 103 ÷ 4 = 25.75

Example 2: 12 1/8

• Method 1: 1/8 = 0.125; 12 + 0.125 = 12.125
• Method 2: (12 * 8 + 1)/8 = 97/8; 97 ÷ 8 = 12.125

Example 3: 5 2/5

• Method 1: 2/5 = 0.4; 5 + 0.4 = 5.4
• Method 2: (5 * 5 + 2)/5 = 27/5; 27 ÷ 5 = 5.4

The Importance of Understanding Decimal Conversions

Mastering the conversion of fractions to decimals is essential for success in various mathematical and real-world applications. The ability to seamlessly switch between these representations enhances problem-solving skills and provides a broader understanding of numerical relationships. By understanding the underlying principles of fraction-to-decimal conversion, you'll be better equipped to tackle more complex mathematical problems. The techniques described above, including long division and the conversion to improper fractions, offer multiple pathways to achieve the same result, allowing you to choose the method most comfortable and efficient for you. Consistent practice and application will solidify your understanding and make this a fundamental skill you can readily apply.