What is the Product of a Decimal and a Whole Number?

S1-SA2-0349

Grade Level:

Class 3

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

The product of a decimal and a whole number is the result you get when you multiply a number with a decimal point (like 2.5) by a number without a decimal point (like 3). It tells you the total when you have a certain fraction of something repeated a whole number of times.

Simple Example

Quick Example

Imagine a small packet of biscuits costs Rs 10.50. If you want to buy 3 such packets, how much will you pay in total? You need to multiply Rs 10.50 (decimal) by 3 (whole number) to find the total cost.

Worked Example

Step-by-Step

Let's find the product of 4.75 and 6.

Step 1: Ignore the decimal point for a moment and multiply the numbers as if they were whole numbers. So, multiply 475 by 6.

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Step 2: Multiply 475 x 6.
475
x 6
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2850

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Step 3: Now, count the number of digits after the decimal point in the original decimal number (4.75). There are two digits (7 and 5) after the decimal point.

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Step 4: In your answer from Step 2 (which is 2850), place the decimal point so that there are the same number of digits after it as you counted in Step 3. So, move the decimal point two places from the right.

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Step 5: Starting from the right of 2850, move the decimal point two places to the left. 28.50

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Answer: The product of 4.75 and 6 is 28.50.

Why It Matters

Understanding this helps in everyday calculations like budgeting pocket money or calculating ingredients for a recipe. It's crucial for careers in finance (calculating interest), engineering (measuring materials), and even data science (working with averages and probabilities).

Common Mistakes

MISTAKE: Forgetting to place the decimal point in the final answer. | CORRECTION: Always count the decimal places in the original decimal number and place the decimal point in the product accordingly.

MISTAKE: Placing the decimal point incorrectly, for example, counting from the left instead of the right in the product. | CORRECTION: The number of decimal places in the product must match the number of decimal places in the original decimal factor, counted from the right end of the product.

MISTAKE: Multiplying the decimal and whole number as separate parts (e.g., multiplying 2 by 3 and 0.5 by 3 for 2.5 x 3, then adding). | CORRECTION: Treat the decimal number as a whole number during multiplication, then place the decimal point in the final product.

Practice Questions

Try It Yourself

QUESTION: What is 3.2 multiplied by 4? | ANSWER: 12.8

QUESTION: A car travels 15.75 km on one litre of petrol. How much distance will it cover on 5 litres? | ANSWER: 78.75 km

QUESTION: You buy 8 pens, and each pen costs Rs 12.25. How much do you pay in total? | ANSWER: Rs 98.00

MCQ

Quick Quiz

What is the product of 7.05 and 3?

21.5

21.15

2.115

211.5

The Correct Answer Is:

Multiplying 705 by 3 gives 2115. Since 7.05 has two decimal places, the product must also have two decimal places, making it 21.15.

Real World Connection

In the Real World

When you buy vegetables at the mandi, the vendor might weigh 1.5 kg of potatoes at Rs 30 per kg. To calculate the total cost, they multiply 1.5 (decimal) by 30 (whole number). Similarly, when calculating your mobile data usage, if you use 0.75 GB every day for 7 days, your total usage is found using this concept.

Key Vocabulary

Key Terms

PRODUCT: The result of multiplication | DECIMAL NUMBER: A number that includes a decimal point, representing parts of a whole | WHOLE NUMBER: A number without fractions or decimals (0, 1, 2, 3, ...) | DECIMAL POINT: The dot in a decimal number that separates the whole number part from the fractional part

What's Next

What to Learn Next

Great job understanding this! Next, you can learn about 'Multiplying a Decimal by a Decimal'. This will build on what you've learned and help you solve even more complex real-world problems involving money, measurements, and more.