What is Multiplying Two Decimals?

S1-SA2-1120

Grade Level:

Class 5

Maths, Finance, Computing, AI, Science

Definition

What is it?

Multiplying two decimals means finding the product when you multiply two numbers that have a decimal point. It's similar to multiplying whole numbers, but you need to carefully place the decimal point in the final answer.

Simple Example

Quick Example

Imagine a small packet of biscuits costs ₹5.50. If you want to buy 3 such packets, you are multiplying ₹5.50 by 3. This is a simple example of multiplying a decimal by a whole number, which is the first step to understanding multiplying two decimals.

Worked Example

Step-by-Step

Let's multiply 2.4 by 1.5.

1. Ignore the decimal points for a moment and multiply the numbers as if they were whole numbers: 24 x 15.
---2. Multiply 24 by 5: 24 x 5 = 120.
---3. Multiply 24 by 10 (which is 24 x 1, shifted one place left): 24 x 10 = 240.
---4. Add these results: 120 + 240 = 360.
---5. Now, count the total number of digits after the decimal point in the original numbers. In 2.4, there is 1 digit after the decimal (4). In 1.5, there is 1 digit after the decimal (5). So, 1 + 1 = 2 digits in total.
---6. Starting from the right of our product (360), move the decimal point 2 places to the left.
---7. 360 becomes 3.60.

So, 2.4 x 1.5 = 3.60 or 3.6.

Why It Matters

Multiplying decimals is crucial for everyday tasks like calculating costs, measuring ingredients, or understanding data. It's used in finance for interest calculations, in science for experiments, and even in computing for precise measurements. Engineers and scientists use this skill daily.

Common Mistakes

MISTAKE: Forgetting to count the total number of decimal places in the original numbers before placing the decimal in the answer. | CORRECTION: Always count the digits after the decimal point in BOTH numbers you are multiplying, then add them up. This sum tells you how many places to move the decimal in your final product.

MISTAKE: Aligning the decimal points when multiplying, similar to how you do it for addition or subtraction. | CORRECTION: When multiplying, you don't need to align the decimal points vertically. Just multiply the numbers as if they were whole numbers first, and then place the decimal point at the very end.

MISTAKE: Incorrectly shifting the decimal point from the left instead of the right in the final product. | CORRECTION: After getting your whole number product, always start from the RIGHTMOST digit and move the decimal point to the LEFT by the total number of decimal places counted.

Practice Questions

Try It Yourself

QUESTION: What is 0.7 x 0.8? | ANSWER: 0.56

QUESTION: A tailor uses 2.5 meters of cloth for one shirt. How much cloth is needed for 1.5 times that amount if a customer wants a special design? | ANSWER: 3.75 meters

QUESTION: A small bottle of sanitiser holds 0.15 litres. If a carton contains 20 such bottles, how many litres of sanitiser are in 0.5 of a carton? | ANSWER: 1.5 litres

MCQ

Quick Quiz

What is the product of 3.2 and 0.4?

12.8

1.28

0.128

128

The Correct Answer Is:

Multiplying 32 by 4 gives 128. There is one decimal place in 3.2 and one in 0.4, making a total of two decimal places. So, we place the decimal two places from the right in 128, resulting in 1.28.

Real World Connection

In the Real World

When you buy groceries, if a vegetable costs ₹45.50 per kg and you buy 0.75 kg (three-quarters of a kg), the shopkeeper uses decimal multiplication to calculate your bill. Many online shopping apps also use this for calculating item costs and discounts precisely.

Key Vocabulary

Key Terms

DECIMAL POINT: A dot separating the whole part from the fractional part of a number | PRODUCT: The result of multiplying two or more numbers | DECIMAL PLACE: The position of a digit to the right of the decimal point | MULTIPLICATION: The process of repeatedly adding a number to itself

What's Next

What to Learn Next

Great job learning about multiplying decimals! Next, you can explore 'Dividing Decimals'. This will build on your understanding of decimal operations and help you solve even more complex real-world problems, like sharing costs or measuring smaller parts.