To calculate the product of 32.97 and 1.07, we simply multiply these two numbers together. Multiplication is a basic arithmetic operation that represents the repeated addition of a number.
Calculation Process
The calculation involves multiplying 32.97 by 1.07. This can be done using a calculator or by hand for those familiar with decimal multiplication. The steps for multiplying decimals by hand are similar to multiplying whole numbers, with the added step of correctly placing the decimal point in the product.
Step-by-Step Calculation
First, we ignore the decimal points and multiply 3297 by 107.
3297 * 100 = 329700
3297 * 7 = 23079
Adding these two results together gives us 329700 + 23079 = 352779.
Next, we determine the total number of decimal places in the factors. Since 32.97 has two decimal places and 1.07 has two decimal places, their product will have 2 + 2 = 4 decimal places.
Therefore, the product of 32.97 and 1.07, with the decimal point correctly placed, is 35.2779.
| Operation | Result |
|---|---|
| Multiplication of 3297 by 107 | 352779 |
| Placement of decimal point | 35.2779 |
Verification and Applications
The result of the multiplication, 35.2779, can be verified using a calculator or a computational tool. This calculation has various applications in finance, science, and engineering, where decimal multiplication is a common operation.
Financial Applications
In finance, such calculations could be used to determine the total cost of goods after applying a discount or markup. For example, if an item costs 32.97 and a 7% sales tax is applied, the total cost would be 32.97 * 1.07 = 35.2779, or 35.28 when rounded to the nearest cent.
In scientific applications, precise calculations are crucial for experiments and data analysis. The ability to accurately multiply decimals is fundamental in these fields.
What is the significance of correctly placing the decimal point in multiplication results?
+Correctly placing the decimal point is crucial because it determines the actual value of the result. Misplacing the decimal point can lead to significant errors, especially in applications where precision is key, such as finance, science, and engineering.
How does one verify the result of a decimal multiplication?
+The result can be verified using a calculator, a computer algebra system, or by manually recalculating the multiplication. It’s also a good practice to estimate the result to ensure it’s within a reasonable range, helping to catch any significant errors.
