To solve the multiplication problem of 1.388 times 3.26, we follow the standard procedure of multiplying decimal numbers. First, we multiply the numbers as if they were whole numbers, and then we count the total number of decimal places in the factors to determine the placement of the decimal point in the product.
Multiplication Steps
We start by multiplying 1.388 by 3.26. To do this, it’s helpful to think of the numbers as 1388 and 326, ignoring the decimal points for the moment.
Actual Multiplication
The multiplication of 1388 by 326 can be broken down into simpler multiplication tasks to make the calculation easier:
1388 * 300 = 416400
1388 * 20 = 27760
1388 * 6 = 8338
Then, we add these results together: 416400 + 27760 + 8338 = 449498.
Determining Decimal Placement
Now, we need to determine where the decimal point goes in our product, 449498. The total number of decimal places in the original factors (1.388 and 3.26) is 5 (3 from 1.388 and 2 from 3.26). Therefore, we place the decimal point in 449498 so that it has 5 decimal places, resulting in 4.54998.
| Factor 1 | Factor 2 | Product |
|---|---|---|
| 1.388 | 3.26 | 4.54998 |
Verification and Application
To verify our calculation, we can use a calculator or perform the multiplication in parts, as shown, and then sum those parts. This step ensures that our manual calculation is correct and reliable.
Real-World Applications
Understanding how to multiply decimal numbers is essential in various real-world applications, including finance, science, and engineering. For instance, calculating the area of a room, the volume of a tank, or the cost of materials for a construction project often involves multiplying decimal numbers.
In finance, decimal multiplication is used to calculate interest rates, investment returns, and currency exchange rates. In science, it's used for measurements and calculations involving physical quantities like speed, acceleration, and density. The ability to accurately perform these calculations is vital for making informed decisions and achieving precise results.
How do I multiply decimal numbers correctly?
+To multiply decimal numbers, first multiply them as if they were whole numbers, ignoring the decimal points. Then, count the total number of decimal places in the factors and place the decimal point in the product accordingly.
Why is it important to correctly place the decimal point in the product of decimal numbers?
+Correctly placing the decimal point is crucial because it determines the actual value of the product. Incorrect placement can lead to significant errors in calculations, which can have serious implications in real-world applications such as finance, science, and engineering.
