What Is 1 And 1/5 As A Decimal

What is 1 and 1/5 as a Decimal? A Comprehensive Guide

Knowing how to convert fractions to decimals is a fundamental skill in mathematics, essential for various applications from everyday calculations to advanced scientific computations. This comprehensive guide will walk you through the process of converting the mixed number 1 and 1/5 into its decimal equivalent, explaining the underlying principles and providing further examples to solidify your understanding. This will cover not only the solution but also delve into the broader concepts of fractions and decimals, ensuring a solid grasp of the subject.

Understanding Fractions and Decimals

Before we tackle the conversion, let's refresh our understanding of fractions and decimals. A fraction represents a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). The denominator indicates how many equal parts the whole is divided into, and the numerator indicates how many of those parts are being considered. For example, 1/5 means one part out of five equal parts.

A decimal, on the other hand, represents a fraction where the denominator is a power of 10 (10, 100, 1000, etc.). The digits to the right of the decimal point represent the tenths, hundredths, thousandths, and so on. For instance, 0.1 represents one-tenth (1/10), 0.01 represents one-hundredth (1/100), and 0.001 represents one-thousandth (1/1000).

Converting 1 and 1/5 to a Decimal: The Steps

The mixed number 1 and 1/5 signifies one whole unit plus one-fifth of a unit. To convert this to a decimal, we'll follow these steps:

Step 1: Separate the Whole Number and the Fraction

First, separate the whole number (1) from the fraction (1/5). We'll convert the fraction to a decimal separately, and then add the whole number back.

Step 2: Convert the Fraction to a Decimal

To convert the fraction 1/5 to a decimal, we need to find an equivalent fraction with a denominator that is a power of 10. In this case, we can easily multiply both the numerator and the denominator by 2 to get:

(1 * 2) / (5 * 2) = 2/10

Now, we can easily express 2/10 as a decimal. The denominator, 10, indicates tenths. Therefore, 2/10 is equal to 0.2.

Step 3: Combine the Whole Number and the Decimal

Finally, combine the whole number (1) with the decimal equivalent of the fraction (0.2):

1 + 0.2 = 1.2

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

Alternative Method: Long Division

Another method to convert a fraction to a decimal is through long division. This method is particularly useful when dealing with fractions that don't easily convert to a denominator that's a power of 10.

To use long division for 1/5:

1. Divide the numerator (1) by the denominator (5).
2. Since 5 doesn't go into 1, add a decimal point to 1 and add a zero to make it 1.0.
3. Now, 5 goes into 10 twice (5 x 2 = 10).
4. The result is 0.2. Adding the whole number back (1), we again get 1.2.

Understanding Decimal Places and Significant Figures

The number 1.2 has one decimal place. The number of decimal places refers to the number of digits after the decimal point. Understanding decimal places is crucial when dealing with measurements and calculations requiring precision. The concept of significant figures also plays a vital role in scientific and engineering applications. Significant figures refer to the digits that carry meaning contributing to its measurement resolution.

In our example, both the 1 and the 2 in 1.2 are significant figures. This indicates a level of precision. If we were dealing with a measurement, this would tell us the accuracy of the measurement.

Further Examples of Fraction to Decimal Conversions

Let's solidify our understanding with a few more examples:

• 2 and 3/4: 3/4 is equivalent to 75/100 (multiply numerator and denominator by 25), which is 0.75. Therefore, 2 and 3/4 is 2.75.

• 3 and 1/8: 1/8 can be converted to 125/1000 (multiply by 125) which is 0.125. Therefore 3 and 1/8 is 3.125.

• 1 and 7/20: 7/20 can be converted to 35/100 (multiply by 5), which equals 0.35. Therefore 1 and 7/20 is 1.35.

These examples demonstrate how the basic principles of converting fractions to decimals can be applied to various situations. Remember to always simplify the fraction to its lowest terms before converting it to a decimal. This will make the calculation easier and avoid unnecessary complexity.

Recurring Decimals

It's important to note that not all fractions convert to terminating decimals (decimals that end). Some fractions result in recurring decimals (decimals with a repeating pattern of digits). For example, 1/3 converts to 0.3333... (the 3 repeats infinitely). These are represented by placing a bar over the repeating digit or digits. For instance, 0.3333... is written as 0.3̅.

Frequently Asked Questions (FAQ)

Q: What if the fraction has a larger numerator than denominator?

A: If the numerator is larger than the denominator, the fraction is an improper fraction. You first convert it to a mixed number (a whole number and a fraction) before converting the fractional part to a decimal. For example, 7/5 is an improper fraction; converting it to a mixed number gives you 1 and 2/5, which, as we've seen, is 1.2.

Q: Can I use a calculator to convert fractions to decimals?

A: Yes, most calculators have a fraction-to-decimal conversion function. Simply enter the fraction and the calculator will provide the decimal equivalent. However, understanding the manual process is essential for grasping the underlying mathematical principles.

Q: Why is it important to learn how to convert fractions to decimals?

A: Converting fractions to decimals is a fundamental skill with practical applications across numerous fields, including:

• Finance: Calculating interest, discounts, and proportions.
• Science: Representing measurements and experimental data.
• Engineering: Designing and building structures and machines.
• Everyday life: Calculating tips, splitting bills, and measuring ingredients.

Conclusion

Converting 1 and 1/5 to a decimal, resulting in 1.2, is a straightforward process once you understand the principles of fractions and decimals. By mastering this conversion method, you'll enhance your mathematical skills and improve your problem-solving abilities in various contexts. Remember to break down complex problems into smaller, manageable steps, and utilize different methods such as long division when necessary. The examples and explanations provided in this guide should equip you with the knowledge and confidence to tackle similar conversions with ease. The ability to move fluidly between fractions and decimals demonstrates a strong understanding of numerical representation and lays a solid foundation for more advanced mathematical concepts.