Multiplication can seem daunting when dealing with decimals, but breaking down the process can make it more manageable. To multiply 459 by 1.075, we can follow a step-by-step approach that simplifies the calculation. First, it's helpful to understand that multiplying by a decimal is similar to multiplying by a whole number, with the added step of placing the decimal point correctly in the final product.
Understanding the Basics of Decimal Multiplication
When multiplying a whole number by a decimal, we can first ignore the decimal point in the multiplier (1.075 in this case) and perform the multiplication as if both numbers were whole numbers. The number 1.075 can be thought of as 1075⁄1000 or simply 1075 when ignoring the decimal for the multiplication step. Thus, we multiply 459 by 1075.
Performing the Multiplication
To multiply 459 by 1075, we follow the standard multiplication procedure:
459 * 1000 = 459,000
459 * 70 = 32,130
459 * 5 = 2,295
Then, we add these results together: 459,000 + 32,130 + 2,295 = 493,425.
However, since we're actually multiplying by 1.075 (which is 1075/1000), we need to adjust our result by dividing by 1000 to account for the decimal place in 1.075. This means our final step is to place the decimal point correctly in 493,425 to reflect the multiplication by 1.075.
| Operation | Result |
|---|---|
| Multiplication without decimal consideration | 493,425 |
| Adjustment for decimal in 1.075 | 493.425 |
Final Calculation and Verification
By following the steps outlined above, we find that 459 multiplied by 1.075 equals 493.425. This calculation can be verified using a calculator or by performing the multiplication in parts and then summing those parts, as demonstrated.
Practical Application and Real-World Examples
In real-world scenarios, such as calculating the total cost of items after a discount or determining the area of a room with decimal measurements, being able to accurately multiply whole numbers by decimals is crucial. For instance, if a store offers a 7.5% discount on all items and you purchase an item priced at 459, you would multiply 459 by 0.075 to find the discount amount, and then subtract that from the original price to get the final cost.
Understanding how to perform such calculations manually not only improves mathematical proficiency but also enhances problem-solving skills in various contexts, including finance, architecture, and science.
How do I ensure the decimal point is in the correct place when multiplying by a decimal?
+To ensure the decimal point is correctly placed, count the total number of decimal places in the multiplier. Then, place the decimal point in the product by shifting it to the left by the same number of places as there are decimal places in the multiplier.
Can I use a calculator to verify my multiplication results?
+Yes, calculators are excellent tools for verifying the results of decimal multiplications. Simply enter the numbers and operation into the calculator, and it will provide the result, helping you confirm the accuracy of your manual calculation.
In conclusion, multiplying 459 by 1.075 involves a straightforward process of ignoring the decimal initially, performing the multiplication, and then adjusting for the decimal place. By mastering this technique, individuals can enhance their mathematical skills, leading to greater confidence and proficiency in handling a wide range of numerical tasks.
