Verified Answer :

  • Identify the total number of decimal places: \(4.07\) has two, \(1.3\) has one, so the result must have three decimal places.
  • Perform integer multiplication: \(407 \times 13 = 5291\).
  • Apply the decimal point to the result: \(5.291\).
  • The final product is \(\boxed{5.291}\).

Explanation

  1. Analyzing Decimal Places

To multiply the two decimal numbers \(4.07\) and \(1.3\), we can treat them initially as whole numbers. First, observe the number of decimal places in each factor. The number \(4.07\) has two decimal places, and the number \(1.3\) has one decimal place. Therefore, the product of these two numbers will have a total of \(2 + 1 = 3\) decimal places.

  1. Multiplying as Integers

Now, we perform the multiplication as if both numbers were integers by ignoring the decimal points: \(407 \times 13\). We can calculate this as:
\[407 \times 13 = 407 \times (10 + 3) = 4070 + 1221 = 5291.\]
The product of the integers is \(5291\).

  1. Placing the Decimal Point

Finally, we place the decimal point back into our result. Since the total number of decimal places required is \(3\), we count three digits from the right of \(5291\) and place the decimal point. Counting three digits from the right gives \(5.291\). Thus, \(4.07 \times 1.3 = \boxed{5.291}\).

Examples

Imagine you are buying fruit at the market. If you need to buy 1.3 kilograms of apples, and the price is \$4.07 per kilogram, you can use decimal multiplication to determine the total cost. By calculating \(4.07 \times 1.3\), you find the exact amount you need to pay, which is \(\$5.291\). In a real store, this would be rounded to the nearest cent as \(\$5.29\). Knowing how to handle decimal multiplication is a vital skill for managing personal finances and making everyday purchases.