Sure, let's carefully examine why the product of [tex]\(0.25 \times 0.8\)[/tex] appears to have only one decimal place in the product.
### Step-by-Step Solution:
1. Identify Decimal Places in Each Factor:
- The number [tex]\(0.25\)[/tex] has 2 decimal places.
- The number [tex]\(0.8\)[/tex] has 1 decimal place.
2. Determine Total Decimal Places in Product:
- The total number of decimal places in the product is the sum of the decimal places in each factor.
- So, [tex]\(2\)[/tex] (from [tex]\(0.25\)[/tex]) [tex]\(+\)[/tex] [tex]\(1\)[/tex] (from [tex]\(0.8\)[/tex]) [tex]\(=\)[/tex] [tex]\(3\)[/tex] decimal places in total.
3. Calculate the Product:
- Now, calculate the actual multiplication: [tex]\(0.25 \times 0.8 = 0.20\)[/tex].
4. Understanding the Representation:
- The product [tex]\(0.20\)[/tex] technically has two decimal places. However, when a decimal number has trailing zeros (zeros after the last non-zero digit), these zeros are often omitted in its standard representation. So, [tex]\(0.20\)[/tex] is typically represented as [tex]\(0.2\)[/tex].
5. Final Representation:
- Therefore, [tex]\(0.25 \times 0.8\)[/tex] appears to have only one decimal place because the trailing zero in [tex]\(0.20\)[/tex] is not displayed, making it look like [tex]\(0.2\)[/tex].
In summary, the apparent single decimal place in [tex]\(0.25 \times 0.8 = 0.2\)[/tex] is due to the omission of the trailing zero in the conventionally displayed decimal representation. The actual value is [tex]\(0.20\)[/tex], but it is simply shown as [tex]\(0.2\)[/tex].
