Juan is solving a multiplication problem where both terms include decimal values. The first term has 5 digits after the decimal and the second term has 3 digits after \( t \)

When multiplying two decimal numbers, it's important to consider the number of digits after the decimal point in each factor. This determines the placement of the decimal point in the final product. **Given:** - **First Term:** A decimal number with **5 digits** after the decimal point. - **Second Term:** A decimal number with **3 digits** after the decimal point. **Steps to Multiply Two Decimals:** 1. **Ignore the Decimal Points:** - Temporarily treat both numbers as whole numbers by removing the decimal points. 2. **Multiply the Numbers:** - Perform the multiplication as you would with whole numbers. 3. **Determine the Total Number of Decimal Places in the Product:** - Add the number of decimal places in both factors. - **Total Decimal Places = 5 (from the first term) + 3 (from the second term) = 8** 4. **Place the Decimal Point in the Product:** - Starting from the right, count 8 digits and place the decimal point there. **Example:** Let's illustrate this with specific numbers. - **First Term:** 12.34567 (5 digits after the decimal) - **Second Term:** 0.789 (3 digits after the decimal) **Step 1: Ignore the Decimal Points** - 12.34567 → 1234567 - 0.789 → 789 **Step 2: Multiply the Whole Numbers** \[ 1234567 \times 789 = 974,085,363 \] **Step 3: Total Decimal Places** - 5 (from 12.34567) + 3 (from 0.789) = **8 decimal places** **Step 4: Place the Decimal Point** - Starting from the right, count 8 digits: \[ 974,085,363 \] - Insert the decimal point 8 digits from the right: \[ \text{9.74085363} \] **Final Product:** \[ 12.34567 \times 0.789 = 9.74085363 \] **Key Takeaway:** - **When multiplying decimals, add the number of digits after the decimal points in both factors to determine the number of decimal places in the product.** - **In this case, the product will have 8 digits after the decimal point.** If you have specific numbers you'd like to multiply or need further clarification, feel free to ask!