Multiplying Decimal by Whole Number

One of the major applications of multiplying decimal by whole number is in the billing of objects when the amount is usually in decimals. Decimals play an important role in our life. They are mostly used in the field of measurement and money where accurate calculations are required. We will be understanding more about multiplying a decimal by a whole number by following some rules and examples.

Multiplying decimals by whole numbers is similar to the multiplication of whole numbers, the only difference is in the placement of the decimal point. Let’s look into the steps below to understand the multiplication of decimal by a whole number.

• Step 1: Multiply the numbers using the normal multiplication method without considering the decimal point initially.
• Step 2: After the multiplication, count the number of decimal places in the given numbers.
• Step 3: The product obtained after multiplication should have the same number of decimal places as given in the numbers. In other words, the decimal point in the product should be placed in such a way that it is equal to the sum of the decimal places of all the multiplicands and the multipliers.

Let us understand the application of multiplication of a decimal number by a whole number.

Example: Five friends go to a cafe and check out the menu to have a burger. They find that a burger costs $5.7. What is the total bill if all of them purchase one burger each?

Solution: The total bill can be calculated if we multiply the cost of one burger by the total number of people, which is 5. Here, we need to multiply a whole number and a decimal, i.e., 5.7 × 5

Therefore, the total bill is $28.5

Multiplying a two-digit whole number by a decimal is as simple as multiplying two whole numbers and placing the points in the final result accordingly. The steps followed will be the same as multiplying a decimal by a whole number as discussed above. Let’s take the example of 1.25 × 15 as shown below.

Here, 1.25 is considered as a whole number 125 without considering the decimal places and multiplied by 15. The product of the two numbers is 1875. Finally, the decimal point is placed in the product by counting the number of places in the decimal 1.25. Since there are two decimal places in 1.25 and 0 decimal places in 15, the decimal point is placed after two places starting from the right in the product 1875. Hence, the result is 18.75

Multiplying a 3 digit whole number by a decimal is quite similar to the normal multiplication of two whole numbers in which the decimal point is placed by counting the decimal places in the given numbers. The steps followed will be the same as multiplying a decimal by a whole number as discussed above. We will understand this by taking an example of the numbers 225 and 5.17 as shown below.

Here, 5.17 is considered as a whole number 517 without considering the decimal places and multiplied by 225. The product of the two numbers is 116325. Finally, the decimal point is placed in the product by counting the number of places in the decimal 5.17. Since there are two decimal places in 5.17 and 0 decimal places in 225, the decimal point is placed after two places starting from the right in the product 116325. Hence, the product is 1163.25

Important Notes:

These are a few key points related to the concept of multiplying decimals by a whole number.

• Multiplication of decimal by a whole number follows the same rules as the multiplication of whole numbers.
• The decimal point in the product should be placed in such a way that it is equal to the sum of the decimal places of all the multiplicands and the multipliers.
• All the zeros in the product have to be retained while placing the decimal point.
• If the product has more decimal places than the number of digits, zeros can be inserted on the left before placing the decimal point in the product.
• The trailing zeros in the resultant product can be dropped.

Related Links:

Check out the following pages related to Multiplying Decimal by Whole Number.

• Multiplication
• Whole Numbers
• Decimals

How to Multiply a Decimal by a Whole Number?

Multiplication of a decimal by a whole number is similar to the regular multiplication done without considering the decimal point initially. The decimal point in the answer is finally placed according to the decimal places given in the numbers. In other words, the decimal point in the product should be placed in such a way that it is equal to the sum of the decimal places of all the multiplicands and the multipliers.

How to Multiply a 2 digit Whole Number by a Decimal?

Multiplication of a 2 digit whole number by a decimal is as simple as multiplying two whole numbers without considering the decimal point. The decimal point in the obtained product is inserted by starting from the right and moving by the number of places equal to the number of places in the given decimal.

Why does Multiplying Numbers by 10 move the Decimal Point to the Right?

When decimal numbers are multiplied with powers of 10, the decimal point in the final product shifts to the right by the number of 0s in the powers of 10. For example, let's take 5.6 and 10. We will multiply these without considering the decimal point, i.e., 56 × 10 = 560. Finally, we place the decimal point after one place starting from the right in the final product as 5.6 has one decimal place. Thus, the result is 56.0 or simply 56. Hence, we see that the number was 5.6 initially and when multiplied with 10, the result obtained was 56 which shows that the decimal point has moved towards the right by one place.

How to Multiply Decimals by Powers of 10?

When a decimal number is multiplied by powers of 10, there's a shift of the decimal point towards the right by an equal number of 0s present in the powers of 10 in the final product. For example, 2.45 × 10² = 2.45 × 100 = 245, here, we see that when 2.45 is multiplied by 10² the result is 245 which shows that the decimal point has shifted towards the right by 2 places. Similarly, in 66.9876 × 10³ = 66.9876 × 1000 = 66987.6, we see that the decimal point in 66.9876 has shifted by 3 places towards the right which gives the result as 66987.6.

How to Multiply Decimals and Fractions?

To multiply decimals and fractions, either the decimal can be converted to a fraction, or, the fraction can be converted to a decimal, and then the multiplication can be easily done. For example, let's take the numbers 0.2 and 3/2, here, 0.2 can be converted to a fraction that is 2/10 or 1/5. Hence, the product is 1/5 × 3/2 = 3/10 or 0.3.

How to Multiply Decimals by Decimals?

Multiplying decimals is as simple as multiplying whole numbers. We multiply the given numbers without considering the decimal points. In the final product, the decimal point is placed in such a way that it is equal to the sum of the decimal places of all the multiplicands and the multipliers. Let's multiply the numbers 1.2 and 2.3. We will multiply these numbers without considering the decimal point, i.e., 12 × 23 = 276. Now, we will finally place the decimal point by two places starting from the right. Hence, 1.2 × 2.3 = 2.76