Multiplying Decimal By Whole Number

To multiply decimals by a whole number, we follow the steps mentioned below:

Step 1: First, we will multiply the number without considering the decimal points. For example, to multiply 12 × 0.5, we first multiply 12 × 5, ignoring the decimal.

Step 2: Next, count the number of decimal places in the original decimal number. 
Here, the product of multiplying 12 × 5 = 60, and the number of decimal places is 1. 

Step 3: The number of decimal points in the product should be equal to the number of decimal points in the original decimal number. In other words, the number of decimal points in the products should be equal to the sum of the decimal points in both the multiplicands and the multipliers.
So, 12 × 0.5 = 6.0. 
 

To multiply decimals by a whole number that has two digits, we follow the steps mentioned below:

Step 1: Ignore the Decimal and Multiply as Whole Numbers
Temporarily ignore the decimal in the decimal number. Treat it as a whole number and multiply it by the two-digit whole number.
For example, Multiply 3.42 × 25
Ignore the decimal in 3.42 and treat it as 342.
Multiply 342 × 25 as if they were whole numbers.

Step 2: Multiply by the Ones Digit
Multiply 342 by the one place of the two-digit number (5 in this case).
342 x 5 = 1710

Step 3: Multiply by the Tens Digit
Multiply 342 by the tens place of the two-digit number (2, which represents 20). Remember to add a zero at the end, since you're multiplying by a multiple of ten.
342 x 20 = 6840

Step 4: Add the Two Partial Products
Now, add the results from Step 2 and Step 3.
1710 + 6840 = 8550

Step 5: Count the Decimal Places
Look at the original decimal number (3.42) and count how many decimal places it has (two decimal places).

Step 6: Place the Decimal in the Final Answer
Since 3.42 has two decimal places, place the decimal two places from the right in the final product.
85.50
Thus, 3.42 × 25 = 85.50 or simply 85.5.
 

To multiply decimals by a whole number that has three digits, we follow the steps mentioned below:

Step 1: Ignore the Decimal and Multiply as Whole Numbers
Remove the decimal from the decimal number and treat it as a whole number. Multiply this number by the three-digit whole number using long multiplication.
For example, Multiply 4.37 × 125
Ignore the decimal and treat 4.37 as 437
Multiply 437 × 125

Step 2: Multiply Using Long Multiplication
Perform long multiplication as usual:

Step 3: Count the Decimal Places
In the original decimal number (4.37), there are two decimal places.
The final product should also have two decimal places.

Step 4: Place the Decimal in the Product
Start from the rightmost digit in 54625 and move two places left to insert the decimal. The final answer is 546.25.
Final Answer: 4.37 × 125 = 546.25
 

Multiplying decimals by whole numbers is used in various fields. Let us discuss some applications of multiplying decimals by whole numbers:

• Shopping and Discounts: When shopping, to calculate the discounts and sales, we multiply decimals by whole numbers. For example, if a store offers a 15% discount on a $12.50 item, you need to find 0.15 × 12.50 to calculate the discount. Similarly, if you buy 4 packs of juice, each costing $2.49, you multiply 2.49 × 4 to determine the total cost. Understanding how to multiply decimals ensures you can accurately calculate savings and expenses while shopping.

• Salary and Wages Calculation: To calculate the salary and wages, we multiply hourly decimal wages by whole numbers to find total pay. 
  For instance, if a worker earns $15.75 per hour and works 40 hours a week, the total weekly wage is calculated as 15.75 × 40 = $630. 
  
   
• Cooking and Recipe Adjustments: When cooking, we need to adjust the ingredients based on the number of servings. If a recipe calls for 1.5 cups of sugar per cake, and you are making 3 cakes, you multiply 1.5 × 3 = 4.5 cups of sugar. This method ensures precise ingredient measurements, leading to consistent and tasty results.