Multiplying Decimal By Whole Number

A key use of multiplying decimals by whole numbers is in billing, where prices often include decimals. Decimals are important in daily life, especially for measurements and money, where precise calculations are needed. We will learn more about multiplying decimals by whole numbers through simple rules and examples.

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 places in the product should match the number of decimal places in the original decimal number.
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).
\(342 × 5 = 1710\)

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 because you are multiplying by a multiple of ten.
\(342 × 20 = 6840\)

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 and treat the number as a whole number. Multiply it 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: \(4.37 × 125 = 546.25\).
 

Learn easy ways to multiply decimals accurately using simple steps. These tricks help improve speed and confidence in solving decimal problems.

• Ignore the decimal first and multiply as whole numbers.
   
• Count the decimal places in the original number.
   
• Place the decimal point in the product correctly.
   
• Estimate your answer to check if it’s reasonable.
   
• Practice with real-life money examples for better understanding.

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, we multiply decimals to find discounts and total prices. For example, a 15% discount on $12.50 or 4 juice packs at $2.49 each can be found by multiplying. This helps you know your savings and total cost easily.

• Salary and wages calculation: To find salary or wages, multiply the hourly pay by the number of hours worked. For example, if someone earns $15.75 per hour and works 40 hours, multiply to get the total pay.
  
   
• Cooking and recipe adjustments: When cooking, we multiply ingredients by the number of servings. For example, if one cake needs 1.5 cups of sugar and you make 3 cakes, multiply to find the total sugar needed. This helps keep the taste and measurements right.
  
   
• Fuel consumption calculation: When calculating fuel costs, we multiply the price per liter (a decimal) by the number of liters purchased. For example, if fuel costs $1.45 per liter and you buy 50 liters, multiplying $1.45 × 50 gives the total cost.
  
   
• Distance and speed: To find the distance traveled, we multiply speed (which can be a decimal) by time. For instance, if a car travels at 65.5 km/h for 3 hours, multiplying 65.5 × 3 gives the total distance covered.