Calculating $7.2 \times 12 \times 0.23$ And Rounding To The Nearest Hundredth

Calculating the product of decimal numbers is a fundamental skill in mathematics, with practical applications in various fields, from finance to engineering. In this article, we will delve into the step-by-step process of solving the equation $7.2 \times 12 \times 0.23$, ensuring a clear understanding of each stage. Our primary goal is to not only find the exact answer but also to master the art of rounding to the nearest hundredth, a crucial skill for real-world scenarios where precision is paramount. This detailed exploration will equip you with the knowledge and confidence to tackle similar problems efficiently and accurately. Let's embark on this mathematical journey together, breaking down each step and understanding the underlying principles. This will not only enhance your calculation skills but also your ability to apply these concepts in practical situations, making you a more proficient problem solver.

Understanding the Basics of Decimal Multiplication

Before diving into the specific calculation, let's reinforce our understanding of decimal multiplication. Decimal multiplication involves multiplying numbers that have a decimal point, representing fractions of a whole. The key to accurately multiplying decimals is to initially ignore the decimal points and treat the numbers as whole numbers. Once you've found the product, you'll need to correctly place the decimal point in the final answer. This placement is determined by counting the total number of decimal places in the original numbers being multiplied. For instance, if you are multiplying 7.2 (one decimal place) by 0.23 (two decimal places), the final product will have three decimal places (1 + 2 = 3). This fundamental concept is the cornerstone of decimal multiplication and must be thoroughly understood to avoid errors. Mastering this principle allows for accurate calculations, which are essential in various fields, including finance, engineering, and everyday transactions. By understanding the underlying mechanics, you'll be able to approach decimal multiplication with confidence and precision. Furthermore, this skill is not just limited to academic exercises; it extends to practical problem-solving in real-world scenarios, making it a valuable asset in your mathematical toolkit.

Step 1 Multiplying $7.2 \times 12$

Our first step in solving the equation $7.2 \times 12 \times 0.23$ is to multiply 7.2 by 12. To do this, we can initially ignore the decimal point and multiply 72 by 12. This simplifies the calculation, allowing us to focus on the core multiplication process. Multiplying 72 by 12 gives us 864. Now, we need to consider the decimal point. In the original number 7.2, there is one decimal place. Therefore, in the product 864, we need to place the decimal point one place from the right, resulting in 86.4. This step-by-step approach ensures accuracy and clarity in the calculation. By breaking down the problem into smaller, manageable parts, we can avoid errors and gain a better understanding of the process. This method is particularly useful when dealing with more complex calculations involving multiple decimal numbers. Understanding this process not only helps in solving the given equation but also provides a foundation for tackling more advanced mathematical problems. The ability to accurately multiply decimals is a crucial skill in various fields, from everyday budgeting to complex scientific calculations. Therefore, mastering this step is essential for mathematical proficiency.

Step 2 Multiplying $86.4 \times 0.23$

Having calculated $7.2 \times 12 = 86.4$, our next step is to multiply 86.4 by 0.23. Again, we can initially ignore the decimal points and multiply 864 by 23. This simplifies the process and allows us to focus on the multiplication itself. The product of 864 and 23 is 19872. Now, we need to account for the decimal points. In the original numbers, 86.4 has one decimal place, and 0.23 has two decimal places. This means that the final product will have a total of three decimal places (1 + 2 = 3). Counting three places from the right in 19872, we place the decimal point to get 19.872. This step is crucial for maintaining accuracy in our calculations. Misplacing the decimal point can lead to significant errors, especially in real-world applications. By carefully counting the decimal places and applying the rule, we ensure that our answer is correct. This meticulous approach is a hallmark of good mathematical practice and is essential for problem-solving in various fields, including science, engineering, and finance. Understanding this process not only helps in solving the given equation but also reinforces the importance of precision in mathematical calculations.

Step 3 Rounding 19.872 to the Nearest Hundredth

The final step in solving the equation is to round 19.872 to the nearest hundredth. The hundredth place is the second digit after the decimal point, which in this case is 7. To round to the nearest hundredth, we need to look at the digit immediately to the right of the hundredth place, which is 2. The rule for rounding is that if the digit to the right is 5 or greater, we round up the hundredth place. If it is less than 5, we leave the hundredth place as it is. In this case, since 2 is less than 5, we do not round up. Therefore, 19.872 rounded to the nearest hundredth is 19.87. This rounding process is essential for providing answers that are both accurate and practical. In many real-world situations, exact answers are not always necessary or meaningful. Rounding allows us to simplify the answer and present it in a way that is easier to understand and use. This skill is particularly important in fields such as finance, where amounts are often rounded to the nearest cent, and in scientific measurements, where precision is balanced with practicality. Understanding the principles of rounding is a fundamental aspect of mathematical literacy and is crucial for effective problem-solving in various contexts.

Final Answer and Conclusion

After meticulously performing the multiplication $7.2 \times 12 \times 0.23$ and rounding the result to the nearest hundredth, we arrive at the final answer of 19.87. This process demonstrates the importance of understanding decimal multiplication and rounding rules, which are essential skills in various mathematical and real-world applications. By breaking down the problem into manageable steps, we can ensure accuracy and clarity in our calculations. The ability to accurately multiply decimals and round them appropriately is a valuable asset in fields such as finance, engineering, and everyday problem-solving. This exercise not only provides the answer to the specific equation but also reinforces the fundamental principles of decimal arithmetic. By mastering these skills, individuals can confidently tackle more complex mathematical challenges and apply these concepts in practical situations. The journey from understanding the basics of decimal multiplication to accurately calculating and rounding the final answer highlights the importance of precision and attention to detail in mathematics. This knowledge empowers individuals to approach mathematical problems with confidence and competence.

Answer

The correct answer is B) 19.87.