Calculate 3.7 X 0.14: Step-by-Step Solution

by Alex Johnson 44 views

Let's dive into the world of decimal multiplication! In this article, we will solve the problem of calculating 3.7 multiplied by 0.14. This kind of problem is a fundamental skill in mathematics, often encountered in everyday situations like calculating costs, measurements, and more. We will break down the calculation step by step, making it easy to understand and follow. So, if you've ever wondered how to multiply decimals or just want to brush up on your math skills, you've come to the right place. Let's embark on this mathematical journey together and discover the solution in a clear and concise manner. Ready to multiply? Let’s get started!

Understanding Decimal Multiplication

Before we jump into the specific calculation, it's essential to grasp the core concept of decimal multiplication. Multiplying decimals might seem daunting at first, but it's actually quite similar to multiplying whole numbers. The key difference lies in handling the decimal points. When multiplying decimals, you initially ignore the decimal points and multiply the numbers as if they were whole numbers. Once you have the product, you count the total number of decimal places in the original numbers and apply that count to the product. This ensures that your final answer is accurate and reflects the true value of the multiplication. Understanding this basic principle is the cornerstone of mastering decimal multiplication. By breaking it down into simpler steps, we can approach even complex calculations with confidence. Keep this in mind as we proceed, and you'll find that multiplying decimals becomes much less intimidating. So, let's delve deeper into how this works with our specific example.

Breaking Down the Numbers: 3.7 and 0.14

To tackle our problem effectively, let's first break down the numbers involved: 3.7 and 0.14. The number 3.7 has one decimal place, meaning there is one digit to the right of the decimal point. On the other hand, 0.14 has two decimal places, as there are two digits after the decimal point. Keeping track of these decimal places is crucial for determining the correct placement of the decimal point in our final answer. Remember, the total number of decimal places in the factors (the numbers we are multiplying) will determine the number of decimal places in the product (the result of the multiplication). In our case, we have a total of three decimal places (one from 3.7 and two from 0.14). This means our final answer will also have three decimal places. By carefully noting these details at the outset, we set ourselves up for an accurate calculation. This is a fundamental step in decimal multiplication, ensuring we don't lose track of the decimal's significance. Now that we have this groundwork laid, let's move on to the actual multiplication process.

Step-by-Step Calculation of 3.7 x 0.14

Now, let's walk through the step-by-step calculation of 3.7 multiplied by 0.14. This will provide a clear understanding of how to arrive at the correct answer.

  1. Ignore the decimal points: Start by treating the numbers as whole numbers. So, instead of multiplying 3.7 by 0.14, we will multiply 37 by 14. This simplifies the initial multiplication process and allows us to focus on the numerical values without the distraction of decimals.
  2. Multiply as whole numbers: Perform the multiplication of 37 by 14.
    • 37 x 4 = 148
    • 37 x 10 = 370
    • Add these results together: 148 + 370 = 518 So, 37 multiplied by 14 equals 518. This is a crucial intermediate step, giving us the numerical value of the product before we account for the decimal places.
  3. Count the decimal places: Remember that 3.7 has one decimal place and 0.14 has two decimal places. This gives us a total of three decimal places in the original numbers. This total is the key to placing the decimal correctly in our final answer.
  4. Place the decimal point: In the product 518, we need to place the decimal point so that there are three digits to the right of it. This means we count three places from the right: 518 becomes 0.518. The placement of the decimal point is the final step in ensuring our answer is accurate. It reflects the scale of the original numbers and provides the correct magnitude for the result.

By following these steps, we can confidently calculate the product of 3.7 and 0.14. The meticulous approach ensures that every aspect of the multiplication, including the decimal placement, is handled correctly. Now, let's see the final answer and discuss its significance.

The Answer: 0.518

After meticulously working through the multiplication steps, we arrive at the answer: 3.7 multiplied by 0.14 equals 0.518. This result is crucial, and it's essential to understand what it represents. The value 0.518 is the product of our two decimal numbers, accurately reflecting their combined value. It's important to note the decimal placement, as it significantly affects the magnitude of the number. If the decimal were placed differently, the answer would be drastically different. This highlights the importance of careful calculation and attention to detail when dealing with decimals. The answer 0.518 is not just a number; it's the solution to our multiplication problem, representing the specific relationship between 3.7 and 0.14. Now that we have our answer, let's explore how it relates to the multiple-choice options provided and confirm its accuracy in the context of the question.

Matching the Answer to the Options

Now that we've calculated that 3.7 multiplied by 0.14 equals 0.518, let's see how this answer aligns with the multiple-choice options provided. Looking back at the options, we have:

  • A. 2.85
  • B. 0.285
  • C. 5.18
  • D. 0.518

Comparing our calculated answer of 0.518 with these options, it's clear that option D, 0.518, is the correct match. This confirms that our step-by-step calculation was accurate, and we've successfully identified the right answer from the given choices. This process of matching the calculated answer to the options is a crucial step in problem-solving, especially in multiple-choice scenarios. It ensures that we not only arrive at the correct numerical value but also correctly identify the corresponding choice. This final verification step solidifies our understanding and provides confidence in our solution. So, we've not only solved the multiplication problem but also successfully navigated the multiple-choice format. Now, let's delve into why understanding decimal multiplication is important in real-world scenarios.

Why Decimal Multiplication Matters

Understanding decimal multiplication isn't just about acing math problems; it's a crucial skill that applies to numerous real-world situations. Think about it – how often do you encounter situations involving decimals in your daily life? The answer is: quite often! From calculating the cost of groceries at the store to figuring out measurements for a DIY project, decimals are everywhere. For instance, when you're buying items that are priced per pound or kilogram, you're dealing with decimal multiplication to determine the total cost. Similarly, in construction or crafting, accurate measurements often involve decimals, and multiplying these measurements is essential for ensuring your project turns out as planned. Even in financial planning, understanding decimal multiplication is key for calculating interest rates or investment returns. The ability to confidently and accurately multiply decimals empowers you to make informed decisions, whether it's managing your finances, tackling home improvement projects, or simply understanding the world around you. So, while it may seem like a simple mathematical concept, decimal multiplication is a fundamental life skill that enhances your problem-solving abilities and helps you navigate everyday challenges. Let’s consider some specific examples to illustrate this further.

Real-World Examples of Decimal Multiplication

To truly appreciate the importance of decimal multiplication, let's explore some real-world examples where this skill comes into play. Imagine you're at the grocery store, and apples are priced at $1.79 per pound. You decide to buy 2.5 pounds of apples. To calculate the total cost, you need to multiply 1.79 by 2.5. This is a perfect example of decimal multiplication in action, helping you determine the price you'll pay at the checkout. Another scenario is calculating fuel efficiency. If your car travels 25.5 miles per gallon and you drive 10.8 gallons, you'd multiply these two decimals to find the total distance you've traveled. This is crucial for planning trips and managing fuel consumption. In the realm of finance, let's say you invest $1,000 in a savings account with an annual interest rate of 2.75%. To calculate the interest earned in a year, you'd multiply $1,000 by 0.0275 (the decimal equivalent of 2.75%). This helps you understand how your investments grow over time. These examples underscore the practical applications of decimal multiplication across various aspects of daily life, from shopping and driving to managing personal finances. By mastering this skill, you gain a valuable tool for navigating these situations with confidence and accuracy. With these practical applications in mind, it’s clear that decimal multiplication is more than just a math concept; it’s a life skill.

Conclusion

In conclusion, we've successfully solved the problem of 3.7 multiplied by 0.14, arriving at the answer of 0.518. We accomplished this by breaking down the calculation into manageable steps, including ignoring the decimal points initially, multiplying as whole numbers, counting the decimal places, and then placing the decimal point correctly in the final product. This meticulous approach ensures accuracy and clarity in our solution. Moreover, we've highlighted the significance of decimal multiplication in real-world scenarios, from everyday tasks like grocery shopping to more complex situations such as financial planning and construction projects. Understanding and applying decimal multiplication is a valuable skill that empowers us to make informed decisions and solve practical problems effectively. So, the next time you encounter decimals in your daily life, remember the steps we've discussed, and you'll be well-equipped to tackle the calculations with confidence. Keep practicing, and you'll find that decimal multiplication becomes second nature, opening up a world of mathematical possibilities. For further learning and practice on decimal multiplication, you can visit trusted educational websites like Khan Academy. They offer a wealth of resources, including tutorials, exercises, and videos, to help you strengthen your understanding of this essential mathematical concept.