What Is 1.375 As A Fraction

What is 1.375 as a Fraction? A Comprehensive Guide

Converting decimals to fractions might seem daunting at first, but with a systematic approach, it becomes a straightforward process. This comprehensive guide will not only show you how to convert 1.375 to a fraction but will also equip you with the knowledge and skills to tackle similar decimal-to-fraction conversions. We'll explore various methods, explain the underlying principles, and provide practical examples to solidify your understanding.

Understanding Decimals and Fractions

Before diving into the conversion, let's briefly review the fundamentals of decimals and fractions.

Decimals: Decimals represent parts of a whole number using a base-ten system. The digits to the right of the decimal point represent tenths, hundredths, thousandths, and so on. For example, in 1.375, the '1' represents one whole unit, the '3' represents three tenths (3/10), the '7' represents seven hundredths (7/100), and the '5' represents five thousandths (5/1000).

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

Method 1: Using the Place Value Method

This is perhaps the most intuitive method for converting terminating decimals (decimals that end) into fractions.

1. Identify the place value of the last digit: In 1.375, the last digit, 5, is in the thousandths place. This means the denominator of our fraction will be 1000.

2. Write the decimal part as the numerator: The decimal part of 1.375 is 375. So, our numerator is 375.

3. Form the initial fraction: This gives us the improper fraction 375/1000.

4. Simplify the fraction: To simplify, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 375 and 1000 is 125. Divide both the numerator and the denominator by 125:

   375 ÷ 125 = 3 1000 ÷ 125 = 8

   This simplifies the fraction to 3/8.

5. Add the whole number: Remember the '1' before the decimal point? We need to add that back in. Since 3/8 is less than 1, we can simply write the final answer as a mixed number: 1 3/8.

Method 2: Using Powers of 10

This method is closely related to the place value method but emphasizes the role of powers of 10.

1. Write the decimal as a fraction over a power of 10: 1.375 can be written as 1375/1000 (since there are three digits after the decimal point, the denominator is 10³ = 1000).

2. Simplify the fraction: Again, we find the GCD of 1375 and 1000, which is 125. Dividing both by 125 gives us 11/8.

3. Convert the improper fraction to a mixed number: 11/8 is an improper fraction (numerator is larger than the denominator). We divide 11 by 8: 11 ÷ 8 = 1 with a remainder of 3. This gives us the mixed number 1 3/8.

Method 3: Repeated Multiplication by 10

This method is particularly useful for dealing with repeating decimals, although it's applicable here as well.

1. Multiply the decimal by a power of 10 to remove the decimal point: Multiply 1.375 by 1000 (since there are three digits after the decimal point) to get 1375.

2. Write this as a fraction: This gives us 1375/1000.

3. Simplify the fraction: As before, simplify 1375/1000 by dividing both the numerator and denominator by their GCD (125) to get 11/8.

4. Convert the improper fraction to a mixed number: 11/8 = 1 3/8.

Why Simplify Fractions?

Simplifying fractions is crucial for several reasons:

• Clarity: Simplified fractions are easier to understand and work with.
• Comparison: It's easier to compare simplified fractions.
• Accuracy: In calculations, simplified fractions lead to more accurate results.
• Standard Form: Presenting fractions in their simplest form is a mathematical convention.

Understanding Improper Fractions and Mixed Numbers

An improper fraction is a fraction where the numerator is greater than or equal to the denominator (e.g., 11/8). A mixed number combines a whole number and a proper fraction (e.g., 1 3/8). Both represent the same quantity, but mixed numbers are often preferred for their readability when dealing with quantities greater than one.

Practical Applications

Converting decimals to fractions is a fundamental skill with various applications in:

• Mathematics: Solving equations, working with proportions, and simplifying expressions.
• Science: Measuring quantities, calculating ratios, and representing data.
• Engineering: Designing structures, calculating dimensions, and ensuring precision.
• Cooking and Baking: Following recipes, adjusting ingredient quantities, and understanding measurements.

Troubleshooting Common Mistakes

• Incorrect Place Value: Carefully identify the place value of the last digit in the decimal to determine the correct denominator.
• GCD Errors: Ensure you find the greatest common divisor accurately. Use a calculator or prime factorization if needed.
• Improper Fraction Conversion: When converting an improper fraction to a mixed number, remember to account for both the whole number and the remaining fraction.

Advanced Decimal-to-Fraction Conversions

While this article focused on converting terminating decimals, the principles can be extended to recurring (repeating) decimals. However, converting recurring decimals to fractions is more complex and requires a different approach involving algebraic manipulation.

Conclusion

Converting 1.375 to a fraction, resulting in the simplified mixed number 1 3/8, is achievable using several straightforward methods. Mastering these methods empowers you to handle various decimal-to-fraction conversions with confidence. By understanding the underlying principles and following the steps carefully, you can successfully navigate this essential mathematical skill. Remember to always simplify your fractions for clarity and accuracy. Practice is key—the more you convert decimals to fractions, the more proficient you'll become.