Explain how Brian placed the decimal point correctly in his product.
[tex]$14.73 \times 0.75=11.0475$[/tex]
Answer (2)
Count the decimal places in each factor.
Add the number of decimal places: 2 + 2 = 4 .
Place the decimal point in the product so that there are four decimal places.
The final answer is 11.0475 .
Explanation
Understanding Decimal Placement Let's break down how Brian correctly placed the decimal point in his calculation 14.73 × 0.75 = 11.0475 . The key is understanding how decimal places behave during multiplication.
Counting Decimal Places First, count the number of decimal places in each factor:
14.73 has two decimal places (the 7 and the 3).
0.75 also has two decimal places (the 7 and the 5).
Adding Decimal Places Next, add the number of decimal places from both factors: 2 + 2 = 4 . This means the product will have a total of four decimal places.
Placing the Decimal Point Now, consider the product without the decimal point: 110475 . Starting from the right, count four places to the left and insert the decimal point. This gives us 11.0475 .
Conclusion Therefore, Brian correctly placed the decimal point by adding the number of decimal places in the factors and applying that total to the product. The final answer is 11.0475 .
Examples
Imagine you're calculating the area of a rectangular garden plot. If the length is 14.73 meters and the width is 0.75 meters, you multiply these two numbers to find the area. Correctly placing the decimal point ensures you get the accurate area, which is crucial for ordering the right amount of soil or fencing. This principle applies in various real-world scenarios, from calculating medication dosages to determining financial amounts, where precision is essential.
Brian correctly placed the decimal point in his product by counting the decimal places in each factor, which totaled four. After multiplying the two numbers, he positioned the decimal point four places from the right in the result. This resulted in the accurate final answer of 11.0475 .
;
