To multiply decimals, we follow three simple steps. First, ignore the decimal points and multiply the numbers as if they were whole numbers. Second, count the total number of decimal places in all the factors. Third, place the decimal point in the product by counting from the right. Let's see an example: multiplying 2.3 by 1.4. First, we multiply 23 by 14, which gives us 322. Next, we count the decimal places: 2.3 has one decimal place, and 1.4 has one decimal place, for a total of two decimal places. Finally, we place the decimal point in our answer by counting two places from the right, giving us 3.22. So, 2.3 times 1.4 equals 3.22.
Let's look at more examples of multiplying decimals. In our first example, we'll multiply 0.5 by 0.4. First, we ignore the decimal points and multiply 5 times 4, which equals 20. Next, we count the decimal places: 0.5 has one decimal place, and 0.4 has one decimal place, for a total of two decimal places. Finally, we place the decimal point by counting two places from the right in our answer 20, giving us 0.20, which simplifies to 0.2. For our second example, let's multiply 1.25 by 0.8. First, we multiply 125 by 8, which equals 1000. Then, we count the decimal places: 1.25 has two decimal places, and 0.8 has one decimal place, for a total of three decimal places. Finally, we place the decimal point by counting three places from the right in our answer 1000, giving us 1.000, which is simply 1.
Let's explore some special cases when multiplying decimals. Case 1: When multiplying by 0.1, 0.01, 0.001, and so on, we can simply move the decimal point to the left by the number of zeros plus one. For example, 5.6 times 0.1 equals 0.56, 5.6 times 0.01 equals 0.056, and 5.6 times 0.001 equals 0.0056. Case 2: When multiplying by 10, 100, 1000, and so on, we move the decimal point to the right by the number of zeros. For example, 5.6 times 10 equals 56, 5.6 times 100 equals 560, and 5.6 times 1000 equals 5600. Case 3: Sometimes the product has fewer digits than the required decimal places. In this case, we add leading zeros before placing the decimal point. For example, when multiplying 0.07 by 0.2, we first multiply 7 by 2 to get 14. We need 3 decimal places in total, but 14 only has 2 digits. So we add a leading zero to get 014, then place the decimal point to get 0.014.
Let's apply our decimal multiplication skills to solve some word problems. Problem 1: A piece of fabric costs $12.50 per yard. How much will 2.5 yards cost? To solve this, we multiply the price per yard by the number of yards. So, $12.50 times 2.5 equals $31.25. This means 2.5 yards of fabric will cost $31.25. Problem 2: A rectangular garden is 4.2 meters long and 3.5 meters wide. What is its area? To find the area of a rectangle, we multiply the length by the width. So, 4.2 meters times 3.5 meters equals 14.7 square meters. Therefore, the area of the garden is 14.7 square meters. These examples show how decimal multiplication is used in everyday situations to calculate costs, areas, and other measurements.
Let's summarize what we've learned about multiplying decimals. First, multiply the numbers as if they were whole numbers, ignoring the decimal points. Second, count the total number of decimal places in all the factors being multiplied. Third, place the decimal point in the product by counting from the right the number of places determined in step two. For special cases, remember that when multiplying by powers of 10 like 10, 100, or 1000, you can simply move the decimal point to the right by the number of zeros. Conversely, when multiplying by 0.1, 0.01, or 0.001, move the decimal point to the left by the number of zeros plus one. If your product has fewer digits than the required decimal places, add leading zeros before placing the decimal point. These rules make decimal multiplication straightforward once you understand the pattern.