Understanding and Solving Multiplication with Decimals: The Product of 12.47 x 3

When it comes to numerical operations, multiplication can sometimes be tricky, especially when decimals are involved. This article will break down the step-by-step process of solving the multiplication problem 12.47 x 3 and provide some insights into how to approach similar problems.

Introduction to Decimal Multiplication

Decimal multiplication is a fundamental arithmetic operation that is essential in various fields, including science, engineering, and finance. To understand how to multiply a decimal number by an integer, it's important to follow a systematic approach. In this case, we are tasked with finding the product of 12.47 x 3.

Step-by-Step Guide to Multiplication

Step 1: Set Up the Multiplication

First, let's lay out the problem in a format that is easy to follow:

```12.47x 3------```

Step 2: Multiply the Numbers

Start by multiplying the number 12.47 by the digit 3, treating it as if it were a whole number:

```12.47x 3------37.41```

This step involves a simple multiplication of each digit by 3, starting from the rightmost digit and moving to the left. Here’s the detailed breakdown:

7 x 3 21 (write 1, carry 2) 4 x 3 12, plus the carried 2 14 (write 4, carry 1) 2 x 3 6, plus the carried 1 7 (write 7) 1 x 3 3 (write 3)

Thus, the result is 37.41.

Step 3: Place the Decimal Point

Since 12.47 is a decimal number, we need to ensure that the product reflects the correct number of decimal places. The number 12.47 has 2 decimal places, so the final product should also have 2 decimal places:

```12.47x 3------37.41```

Understanding the Final Product

The product of 12.47 x 3 is 37.41. This means that when you multiply 12.47 by 3, you get 37.41. This result can be expressed using LaTeX as:

dfrac{3120050-3}{100} dfrac{3600150-9}{100} dfrac{3741}{100} boxed{37.41}

Conclusion

Multiplying decimals by integers can be straightforward once you follow a systematic approach. By breaking down the problem into smaller, manageable steps, you can ensure accuracy and develop a better understanding of the process. Whether you're working on a homework assignment or a more complex problem in a professional setting, mastering decimal multiplication is a valuable skill.

Additional Resources

If you need more practice or further explanation, consider exploring additional resources such as educational websites, math tutorials, or practice problems to reinforce your understanding.