To multiply 0.4662 by 67, we can follow a simple step-by-step process. First, let's understand that multiplying a decimal number by an integer involves the same process as multiplying two integers, with the added step of correctly placing the decimal point in our final product.
Multiplication Steps
We begin by multiplying 0.4662 by 67. To simplify, we can ignore the decimal point for now and multiply 4662 (which is 0.4662 without the decimal point) by 67.
Calculation
The calculation involves multiplying each digit of 4662 by 67 and then adding up the partial products. However, for simplicity and accuracy, using a calculator or a straightforward multiplication method is advisable.
Let's calculate:
4662 * 67 = 312414
Placing the Decimal Point
Since we originally ignored the decimal point in 0.4662, we must now correctly place it in our product, 312414. Given that 0.4662 has four digits after the decimal point, our product should have its decimal point placed four positions from the right, resulting in 31.2414.
| Operation | Result |
|---|---|
| Multiplying 4662 by 67 | 312414 |
| Placing the decimal point | 31.2414 |
By following these steps, we find that 0.4662 multiplied by 67 equals 31.2414. This method can be applied to any multiplication problem involving decimals, emphasizing the importance of correctly placing the decimal point in the final product.
Real-World Application
Understanding how to multiply decimals is crucial in various real-world applications, including finance, science, and engineering. For instance, in finance, calculating the interest on a loan or the return on an investment often involves multiplying decimal numbers. In science, measurements and calculations frequently require dealing with decimal numbers, making this skill fundamental for accurate analysis and problem-solving.
Example in Finance
Consider a scenario where an investor wants to calculate the interest earned on a 0.4662 million investment over a year, with an annual interest rate of 67% (for simplicity, though such high rates are unusual). The calculation would be 0.4662 million * 67% = 0.4662 million * 0.67. Using the method described, this calculation becomes 466200 * 0.67 = 312414, or 0.312414 million.
Example in Science
In a scientific experiment, if a substance’s volume is 0.4662 liters and it needs to be scaled up by a factor of 67, the total volume required would be 0.4662 liters * 67 = 31.2414 liters, following the same calculation method.
What is the most accurate method for multiplying decimal numbers by integers?
+The most accurate method involves ignoring the decimal point during the multiplication process and then correctly placing it in the final product based on the original position in the decimal number.
Why is it crucial to correctly place the decimal point in the product of a decimal number and an integer?
+Correctly placing the decimal point ensures the accuracy of the calculation, as it directly affects the value of the final product. Incorrect placement can lead to significant errors in calculations, especially in critical applications like finance and science.
In conclusion, multiplying 0.4662 by 67, or any similar problem, involves straightforward multiplication followed by careful placement of the decimal point. This process is fundamental in various fields and ensures the accuracy of calculations.
