What Is 7.2 As A Fraction

What is 7.2 as a Fraction? A Comprehensive Guide

Understanding how to convert decimals to fractions is a fundamental skill in mathematics. This comprehensive guide will walk you through the process of converting the decimal 7.2 into a fraction, explaining the steps in detail and exploring related concepts to build a strong foundation in this area. We'll delve into the intricacies of decimal-to-fraction conversion, covering various methods and providing examples to solidify your understanding. By the end of this article, you'll be able to confidently convert not just 7.2, but any decimal number into its fractional equivalent.

Understanding Decimals and Fractions

Before diving into the conversion process, let's briefly revisit the concepts of decimals and fractions.

Decimals: Decimals represent numbers that are not whole numbers. They use a decimal point to separate the whole number part from the fractional part. For example, in the decimal 7.2, '7' is the whole number part, and '.2' is the fractional part.

Fractions: Fractions represent parts of a whole. They consist of a numerator (the top number) and a denominator (the bottom number). The numerator indicates the number of parts considered, and the denominator indicates the total number of equal parts the whole is divided into. For instance, 1/2 represents one out of two equal parts.

Converting 7.2 to a Fraction: Step-by-Step Guide

The conversion of 7.2 to a fraction involves several straightforward steps:

Step 1: Write the decimal as a fraction with a denominator of 1.

This is the initial step in converting any decimal to a fraction. We can write 7.2 as:

7.2/1

Step 2: Multiply both the numerator and denominator by a power of 10 to remove the decimal point.

The goal here is to eliminate the decimal point. Since there's one digit after the decimal point in 7.2, we multiply both the numerator and denominator by 10 (10¹):

(7.2 x 10) / (1 x 10) = 72/10

Step 3: Simplify the fraction (reduce to its lowest terms).

Now we need to simplify the fraction 72/10 by finding the greatest common divisor (GCD) of both the numerator and the denominator. The GCD of 72 and 10 is 2. Dividing both the numerator and the denominator by 2, we get:

72 ÷ 2 / 10 ÷ 2 = 36/5

Therefore, 7.2 as a fraction is 36/5.

Alternative Method: Understanding Place Value

Another approach to converting 7.2 to a fraction leverages the understanding of place value. The digit '2' in 7.2 is in the tenths place, meaning it represents 2/10. Therefore, we can write 7.2 as:

7 + 2/10

Now, we need to convert the whole number 7 into a fraction with a denominator of 10. We do this by multiplying 7 by 10/10:

(7 x 10)/10 = 70/10

Adding this to 2/10, we get:

70/10 + 2/10 = 72/10

Again, simplifying this fraction by dividing both numerator and denominator by their GCD (2) gives us:

72/10 = 36/5

This confirms our previous result.

Converting Other Decimals to Fractions

The methods outlined above can be applied to convert any decimal number into a fraction. Let's explore a few more examples:

Example 1: Converting 0.75 to a fraction

1. Write as a fraction: 0.75/1
2. Multiply by 100 (since there are two digits after the decimal): (0.75 x 100) / (1 x 100) = 75/100
3. Simplify: The GCD of 75 and 100 is 25. 75 ÷ 25 / 100 ÷ 25 = 3/4

Therefore, 0.75 as a fraction is 3/4.

Example 2: Converting 2.375 to a fraction

1. Write as a fraction: 2.375/1
2. Multiply by 1000 (three digits after the decimal): (2.375 x 1000) / (1 x 1000) = 2375/1000
3. Simplify: The GCD of 2375 and 1000 is 125. 2375 ÷ 125 / 1000 ÷ 125 = 19/8

Therefore, 2.375 as a fraction is 19/8. This can also be expressed as a mixed number: 2 3/8.

Mixed Numbers and Improper Fractions

In the previous example, we encountered an improper fraction (19/8), where the numerator is larger than the denominator. Improper fractions can be converted to mixed numbers, which consist of a whole number and a proper fraction.

To convert 19/8 to a mixed number, we divide the numerator (19) by the denominator (8):

19 ÷ 8 = 2 with a remainder of 3

This means 19/8 is equal to 2 and 3/8, written as 2 3/8.

Conversely, mixed numbers can be converted to improper fractions. To convert 2 3/8 to an improper fraction, we multiply the whole number (2) by the denominator (8) and add the numerator (3):

(2 x 8) + 3 = 19

This becomes the new numerator, and the denominator remains the same: 19/8.

Dealing with Repeating Decimals

Converting repeating decimals to fractions requires a slightly different approach. Repeating decimals are decimals where one or more digits repeat infinitely. For example, 0.333... (where the 3 repeats infinitely) is a repeating decimal. Converting these to fractions involves algebraic manipulation, which is beyond the scope of this introductory guide. However, it's important to be aware that this is a separate process.

Practical Applications of Decimal-to-Fraction Conversion

The ability to convert decimals to fractions is crucial in various fields, including:

• Engineering and Construction: Precise measurements often require fractional representation.
• Cooking and Baking: Recipes frequently use fractional measurements.
• Finance: Calculations involving percentages and interest rates often involve fractions.
• Science: Data analysis and scientific calculations may require expressing numbers as fractions.

Conclusion

Converting decimals to fractions is a vital mathematical skill with practical applications across diverse fields. The step-by-step method outlined in this article provides a clear and straightforward approach for converting decimals, including those with whole number components, into their fractional equivalents. By mastering this skill, you'll enhance your mathematical proficiency and gain a deeper understanding of number representation. Remember to always simplify your fractions to their lowest terms for the most accurate and concise representation. With practice and consistent application, you'll find converting decimals to fractions becomes second nature.