NCERT Solutions for Class 7 Maths: Fractions and Decimals Exercise 2.6

What is Multiplication of Decimals?

Multiplying decimals might seem tricky, but it's just an extension of the multiplication you already know. The most important part is figuring out where to put the decimal point in the final answer. Think of it this way: when you multiply 0.5 by 4, you are essentially adding 0.5 four times: 0.5 + 0.5 + 0.5 + 0.5 = 2.0. The multiplication 0.5 × 4 gives you the same result, 2.0, much faster. The key idea is to first multiply the numbers as if they had no decimal points. So, for 1.2 × 0.3, you would first calculate 12 × 3 = 36. Then, you count the total number of digits after the decimal point in the original numbers (one in 1.2, and one in 0.3, for a total of two). Finally, you place the decimal point in your answer (36) so that it has two decimal places, which gives you 0.36. That's the whole secret!

How to Multiply Decimal Numbers: A Step-by-Step Guide

1. Step 1: Ignore the Decimals and Multiply — First, remove the decimal points from the numbers and multiply them as if they were whole numbers. For example, to multiply 3.5 by 1.2, you would first calculate 35 × 12.
2. Step 2: Count the Total Decimal Places — Go back to the original numbers. Count the total number of digits that are to the right of the decimal point in both numbers combined. In our example, 3.5 has one decimal place, and 1.2 has one decimal place. So, the total is 1 + 1 = 2 decimal places.
3. Step 3: Place the Decimal Point in the Product — Take the product you calculated in Step 1 (35 × 12 = 420). Starting from the rightmost digit, move the decimal point to the left by the total number of places you counted in Step 2. Here, we move it 2 places to the left. So, 420 becomes 4.20. Therefore, 3.5 × 1.2 = 4.20 or 4.2.

Worked Examples: Multiplying Decimals

• Example 1: Multiply a decimal by a whole number (Find 2.71 × 5) Step 1: Multiply without decimals: 271 × 5 = 1355. Step 2: Count decimal places in the original numbers. 2.71 has two decimal places. 5 has zero decimal places. Total = 2. Step 3: Place the decimal point in the answer. Start from the right of 1355 and move two places to the left: 13.55. Final Answer: 13.55
• Example 2: Multiply a decimal by another decimal (Find 0.5 × 0.05) Step 1: Multiply without decimals: 5 × 5 = 25. Step 2: Count decimal places. 0.5 has one decimal place. 0.05 has two decimal places. Total = 1 + 2 = 3. Step 3: Place the decimal point. The answer 25 has only two digits. We need three decimal places, so we add a zero in the front: 0.025. Final Answer: 0.025
• Example 3: Multiply a decimal by 100 (Find 153.7 × 100) This is a special case. To multiply by 100 (which has two zeros), simply shift the decimal point two places to the right. 153.7 becomes 15370. (We add a zero as a placeholder). Final Answer: 15370

Exam Tip: The Fast Way to Multiply by Powers of 10

Remember this simple trick for your exams to save a lot of time! When you multiply a decimal number by 10, 100, 1000, or any other power of 10, you don't need to do the full multiplication process.

Just count the number of zeros in the power of 10 and shift the decimal point to the right by that many places.

• To multiply by 10 (1 zero), shift the decimal 1 place to the right. (e.g., 2.345 × 10 = 23.45)
• To multiply by 100 (2 zeros), shift the decimal 2 places to the right. (e.g., 2.345 × 100 = 234.5)
• To multiply by 1000 (3 zeros), shift the decimal 3 places to the right. (e.g., 2.345 × 1000 = 2345)

Practice Questions with Solutions

• Q: Find the product: 8 × 4.6 A: Step 1: Multiply the numbers without considering the decimal point. 8 × 46 = 368. Step 2: Count the total number of decimal places in the original numbers. 4.6 has one decimal place. 8 has zero decimal places. The total is 1. Step 3: Place the decimal point in the product (368) so that it has one decimal place. Start from the right and move one place to the left. Final answer: 36.8
• Q: Find the product: 2.5 × 0.3 A: Step 1: Multiply the numbers as whole numbers: 25 × 3 = 75. Step 2: Count the total decimal places in the original numbers. 2.5 has one decimal place and 0.3 has one decimal place. Total decimal places = 1 + 1 = 2. Step 3: Place the decimal point in the product (75) so that it has two decimal places. Start from the right and move two places to the left. Final answer: 0.75
• Q: Find: 0.03 × 1000 A: Step 1: Identify that we are multiplying by a power of 10 (1000 has 3 zeros). Step 2: The shortcut is to move the decimal point to the right by the number of zeros. We need to move the decimal point in 0.03 three places to the right. Step 3: Shifting one place gives 0.3. Shifting two places gives 3. To shift a third time, we add a zero. So, 3 becomes 30. Final answer: 30
• Q: A car covers a distance of 89.1 km in one litre of petrol. How much distance will it cover in 10 litres of petrol? A: Step 1: We need to find the total distance for 10 litres. This means we have to multiply the distance covered in one litre by 10. Distance = 89.1 km/litre × 10 litres. Step 2: To multiply 89.1 by 10, we can use the shortcut. Since 10 has one zero, we shift the decimal point one place to the right. Step 3: Shifting the decimal in 89.1 one place to the right gives 891. Final answer: The car will cover 891 km in 10 litres of petrol.

Frequently Asked Questions