Performing multiplication operations with decimals can be straightforward using the right approach. To solve the multiplication of 32.97 by 1.07, we will follow the standard procedure for multiplying decimal numbers. This involves multiplying the numbers as if they were whole numbers and then placing the decimal point in the correct position based on the total number of decimal places in the factors.
Understanding Decimal Multiplication
When multiplying decimal numbers, it’s essential to remember that the decimal point’s position in the product depends on the sum of the decimal places in the factors. For 32.97 and 1.07, we have a total of 4 decimal places (2 in 32.97 and 2 in 1.07). After multiplying the numbers as if they were whole, we will place the decimal point in the product so that it reflects this total count of decimal places.
Step-by-Step Calculation
To calculate 32.97 times 1.07:
- Ignore the decimal points and multiply 3297 by 107.
- Perform the multiplication: 3297 * 100 = 329700, 3297 * 7 = 23079. Adding these gives 352779.
- Now, considering the total decimal places from the original numbers (4 places), we place the decimal point in the product. Starting from the right, we count 4 places and insert the decimal point: 35.2779.
| Operation | Result |
|---|---|
| Multiplication without decimals | 3297 * 107 = 352779 |
| Placing the decimal point | 35.2779 |
The calculation demonstrates a simple yet effective method for multiplying decimal numbers. By following this approach, you can easily solve multiplication problems involving decimals, such as 32.97 times 1.07, which equals 35.2779.
Real-World Applications
Multiplication of decimals is a common operation in various real-world scenarios, including finance, science, and everyday calculations. For instance, calculating the total cost of items when both the price per item and the quantity are expressed in decimals requires this operation. Understanding how to perform decimal multiplication accurately is essential for making precise calculations in these contexts.
Financial Example
Consider a scenario where you are purchasing 1.07 pounds of a product that costs 32.97 per pound. To find the total cost, you would multiply the cost per pound by the number of pounds purchased, which is the same calculation as our initial problem: 32.97 * 1.07 = 35.2779. Rounding to two decimal places (as is standard with currency), the total cost would be approximately $35.28.
How do I ensure accuracy when multiplying decimals?
+To ensure accuracy, always count the total number of decimal places in the factors and apply this count to place the decimal point in the product correctly. Double-checking your calculations and the position of the decimal point can help prevent errors.
What are common mistakes to avoid when multiplying decimals?
+Common mistakes include incorrectly placing the decimal point in the product and not considering the total number of decimal places in the factors. Always perform the multiplication as if the numbers were whole, then adjust the decimal point based on the total decimal places.
In conclusion, multiplying decimal numbers like 32.97 by 1.07 involves a straightforward process of treating the numbers as whole, performing the multiplication, and then correctly placing the decimal point based on the total decimal places in the factors. This approach ensures accuracy and is applicable to a wide range of real-world calculations.
