Multiplying Decimals With Solved Examples.

Overview

Multiplying decimals is very important when we talk about the grouping of items. The multiplication of decimals is an extremely crucial part of fundamental mathematics. It is essential when we are dealing with the grouping of items. Very few steps are involved while we multiply decimals. In this article, we will cover all the concepts related to decimal multiplication and learn many tips and tricks to find the result more quickly than others.

Before learning how to multiply decimals, let us first revise everything we know about decimals. Decimals are a form of a number in Algebra that has two parts. The part ahead of the decimal point is the whole number, and the part behind the decimal point is the fractional part. The decimal point is the dot between the full number and the fractions section. A decimal number, for example, is 3.121453.

Why do We Need to Multiply Decimals

Decimal multiplication is of utmost importance when we multiply fractional parts with whole numbers in real-life situations. Assume you have to give each child present at your party about 0.15 of the cake and there are a total of 20 children. How many equal numbers of cake pieces do you require? For such a case, you need to multiply 0.15 with 20. 

The overall number of decimal places in the resulting number equals the number of decimal places in the numbers being multiplied. When multiplying decimals, leave out the decimal point and multiply the numbers. Apply the decimal point when the multiplication is complete. 

How do you Multiply Decimals? 

The process for multiplying decimals is identical to that for multiplying whole numbers, with the exception of where the decimal point is placed in the result. We frequently encounter situations in daily life when we must perform the multiplication operation on two integers, either one or both of which are decimal numbers. 

How to Multiply Decimals?

Multiplying decimals follows the same steps as multiplying whole integers, except for the decimal point being placed in the product. Further in this article, you will learn how to multiply decimals by whole numbers and multiply decimals with another decimal. 

Multiplying Decimals with Whole Numbers

Multiplying decimals by whole numbers is as easy as multiplying two whole numbers. The only thing to remember here is the decimal point placement after successful multiplication. Read and practice the steps mentioned below to learn the multiplication of decimals by whole numbers.

• Step 1: Take the numbers to be multiplied together and ignore the decimal point. But remember the position of the point in the decimal number. 
• Step 2: Multiply the numbers together.
• Step 3: Place the decimal point exactly where it was present in the original decimal number. This is done to maintain the position of the decimal point. 

See the example written below to understand these steps.

Example: A class has 20 students who decided to pay for the field trip of one of their friends. The students decided to contribute $9.5 each. What is the total contribution of the class?

Solution: The total number of students is 20, out of which one student cannot pay the fees. Hence, 19 students contributed $9.5 each.

The total number of money collected:

Step 1: 19 x 9.5 (ignore the decimal and multiply in next step)

Step 2: 19 x 95 = 1805

Step 3: The decimal point was after one’s place; hence the answer is $180.5 

Hence the total contribution made by the students was $180.5.

Examples of Multiplying Decimals by Whole Numbers

We’ve all encountered situations where we need to multiply two integers, at least one of which is a decimal number, in our daily lives.

Example 1: Suppose you dine with your friend at McDonald’s and buy a mega combo meal of $7.25 each. You both enjoy your meal, and it’s time for the payment. Help your friend calculate the total amount to be paid. To find the bill at Mcdonald’s, just multiply 7.25 with 2. You get 7.25 x 2 = $14.5 to pay at the restaurant. 

Example 2: Assume you want to gift your spouse a bouquet for your anniversary. You plan to buy roses, and each rose costs $0.25. You bought 12 roses and went to the cashier for the bill. What will be the total amount you will pay? To get the total cost of the bouquet multiplied by $0.25 by 12. We get 12 x 0.25 = $3. 

Multiplying Decimals by ten and its Multiples

Multiplying any decimal number with ten and its multiples is quite fascinating. You don’t have to take a pen and paper or a calculator to find the result in such cases. This can be done mentally just by shifting the position of the decimal point to the right. As many zeros are present, the decimal point is often shifted. For instance: 

• When a number is multiplied by 10, the decimal point shifts right one time. This is because 10 has only one zero. 
• When a number is multiplied by 100, you must shift the decimal two times to the right because 100 has two zeros. 
• Can you predict how many times the zero will shift if the number is multiplied by 1000? Yes! Three times. 

For example, 

1.3832 × 10 = 13.832

1.3832 × 100 = 138.32

1.3832 × 1000 = 1383.2

You can see how the decimal point is shifting.

Multiplying Two Decimals Numbers

This section will assist you in learning how to multiply two decimal integers. The process is the same as we studied in the previous section. The only exception that we have is to add the total number of decimal places in both numbers. And then place the decimal point accordingly, which must equal the resultant number’s decimal place. Follow the steps below to multiply two decimals:

• Step 1: Write the numbers to be multiplied together and forget about the decimal point. 
• Step 2: Multiply the two numbers. 
• Step 3: Now count the number of decimal places in the first and second numbers. Add them and place the decimal point in the result of step 2. The decimal point is kept at the point specified by adding the total number of decimal points.

Look at the stepwise example below to better understand this concept.

Example: Multiply 2.49 and 0.53

Solution:

Step 1: Write the numbers to be multiplied. 2.49 x 0.53

Step 2: Ignore the decimal point and multiply the numbers. 249 x 53 = 13197.

Step 3: Add the total number of decimal points. 2 in 2.49 and 2 in 0.53 = 4.

            Place the decimal in the result before four places. 1.3197. 

Thus the multiplication of 2.49 x 0.53 = 1.3197

Expert Tips

Below is the compiled list of tips that can help you summarize the concepts learned in this article:

• The process for multiplying decimals is the same as for multiplying whole integers.
• The decimal point must be put in the product so that the total number of decimal places equals the sum of decimal places in all multiplicands and multipliers.
• When placing the decimal point, make careful to maintain all of the zeros in the product.
• If the number of decimal places in the product exceeds the number of digits, 0s can be added to the left before inserting the decimal point.

Examples for Better Understanding

Example 1: Martin works in a company that pays him $15 .15 per hour. According to the records, he worked 30 hours last week. Calculate the amount of money earned at the end of the week?

Solution: Martin pay per hour = $15 .15 

               Total hours he worked in a week = 30

               The total amount at the end of the week→ 

                Step 1: $15 .15 x 30 (write the values to be multiplied)

                Step 2: Ignore the decimal and multiply 1515 x 30 = 45450

                Step 3: Mark the decimal point after 2 places = $ 454.50

Alternative method

You can also solve this by first multiplying 15.15 by 10. This will shift the decimal point 1 place from the right. Now you have to multiply 151.5 by 3 = 454.5, which is the same as the result above. 

Example 2: A bike travels at the speed of 43.3 miles per hour and takes a total time of 4 hours and 30 mins. Find the distance traveled by bike. 

Solution: The speed of the bike is 43.3 m/h

                 Time taken for travel is 4 hours and 30 min = 4.5 hours

                 From speed distance formula we get that 

                 Distance = speed x time 

                                = 43.3 x 4.5

Step 1: 43.3 x 4.5 (write the multiplying decimal values)

Step 2: Ignore the decimal point and multiply the values. 433 x 45 = 19485

Step 3: Mark the decimal point after two places (because 43.3 has one decimal place and 4.5 also has one decimal place. Hence the sum of both decimal places is 2)= 194.85 miles

Hence the distance traveled by bike is 194.85 miles. 

Frequently Asked Questions 

Q1.What is the formula for dividing a decimal number by a whole number? 

Ans: Follow the instructions below to multiply a decimal value by a whole number: 

Step 1: Multiply both amounts without considering the decimal point. 

Step 2: Determine how many decimal places there are in the decimal number. 

Step 3: Next, insert the decimal point into the product so that both the product’s number of decimal places and the original decimal number match. 

Q2. Do you know how to multiply decimals by 1000? 

Ans: Because there are three zeros in 1000, you must move the decimal point three positions to the right in order to multiply decimals by 1000. 

Q3. What is the Decimal Multiplication Rule? 

Ans: The guidelines for multiplying decimals are as follows: 

Decimal multiplication rules: 

• As with whole numbers, multiply in a similar manner. 
• If the product contains more decimal places than the number of digits, zeros can be added before the decimal point such that there is only one zero to the left of the decimal point and the product’s decimal places equal the sum of the decimal places in the two integers. 
• The product’s decimal point should be positioned so that it has as many decimal places as all of the multiplicands and multipliers combined. 

• The resultant product’s fractional portion can be computed without the trailing zeros. 

Q4. Do you know how to multiply decimals by less than one? 

Ans: Follow these steps to multiply two decimals that are less than one: 

Step 1: First, multiply the two integers regularly without considering the decimal point. 

Step 2: Count the total number of decimal places in the multiplicand and the multiplier after the multiplication. This total number of decimal places will be present as the result of multiplication. 

Step 3: Add a decimal point to the result obtained in Step 2 to complete the calculation. 

As an illustration, 0.5 x 0.2 = 0.10