Multiplication is a fundamental mathematical operation that involves the repeated addition of a number. In this case, we will be simplifying the multiplication of 37.35 and 0.20. To start, it's essential to understand the concept of multiplying decimal numbers. When multiplying decimals, we multiply the numbers as if they were whole numbers, and then count the total number of decimal places in the factors to determine the decimal place in the product.
Multiplication of 37.35 and 0.20
To multiply 37.35 and 0.20, we can follow these steps: First, multiply 37.35 and 0.20 as if they were whole numbers: 3735 * 20 = 74700. Next, count the total number of decimal places in the factors. In this case, 37.35 has 2 decimal places, and 0.20 has 2 decimal places, for a total of 4 decimal places. Finally, place the decimal point in the product so that it has the same number of decimal places as the total number of decimal places in the factors. In this case, the product 74700 will have 4 decimal places, resulting in 7.4700.
Actual Calculation
The calculation can be broken down as follows: 37.35 * 0.20 = 7.47 This result can be obtained by multiplying the numbers and then placing the decimal point in the correct position.
| Factor 1 | Factor 2 | Product |
|---|---|---|
| 37.35 | 0.20 | 7.47 |
Importance of Accurate Decimal Placement
Accurate decimal placement is vital in mathematical calculations, especially when dealing with financial or scientific applications. In the case of the multiplication of 37.35 and 0.20, incorrect decimal placement could result in a significant error. For instance, if the decimal point were placed one position to the right, the result would be 74.70, which is substantially different from the correct result of 7.47.
Real-World Applications
The multiplication of decimal numbers has numerous real-world applications. For example, in finance, decimal multiplication is used to calculate interest rates, investment returns, and currency exchange rates. In science, decimal multiplication is used to calculate measurements, such as the area of a surface or the volume of a substance.
In the context of the multiplication of 37.35 and 0.20, this calculation could be used in a variety of scenarios, such as calculating the cost of goods or services. For instance, if a company is purchasing 37.35 units of a product at a cost of $0.20 per unit, the total cost would be $7.47.
What is the rule for multiplying decimal numbers?
+The rule for multiplying decimal numbers is to multiply the numbers as if they were whole numbers, and then count the total number of decimal places in the factors to determine the decimal place in the product.
Why is accurate decimal placement important in mathematical calculations?
+Accurate decimal placement is crucial in mathematical calculations because it ensures the accuracy of the result. Incorrect decimal placement can result in significant errors, especially in financial or scientific applications.
In conclusion, the multiplication of 37.35 and 0.20 is a straightforward calculation that requires attention to decimal placement. By following the rules for multiplying decimal numbers and placing the decimal point in the correct position, we can ensure the accuracy of the result. This calculation has numerous real-world applications, including finance and science, and is an essential skill for anyone working with numbers.
