CBSE Class 6 Maths: Decimals - Exercise 8.6 Explained

Understanding Decimals in Real Life

Decimals are everywhere around us! Think about money: ₹50.75 is a decimal number, representing 50 rupees and 75 paise. When you measure your height as 1.45 meters, or the weight of vegetables as 2.5 kilograms, you are using decimals. They help us represent parts of a whole number more precisely than fractions in many practical situations. For example, if you have ₹100 and spend ₹25.50, you need to subtract decimals to find out how much money you have left. This exercise, Decimals Ex 8.6, specifically trains you to handle such situations by focusing on the subtraction of decimal numbers. It's not just about textbook problems; it's about building a skill you'll use constantly!

Key Steps for Subtracting Decimals

Subtracting decimals might seem a bit tricky at first, but it's very similar to subtracting whole numbers. The most important rule to remember is to align the decimal points vertically. Think of it like making sure your hundreds column aligns with hundreds, and tens with tens. Similarly, the decimal point must line up perfectly. This ensures that you are subtracting tenths from tenths, hundredths from hundredths, and so on. If one number has fewer decimal places than the other, you can add trailing zeros to the end of the number to make the number of decimal places equal. This helps in keeping the place values correctly aligned and prevents errors during subtraction, especially when borrowing. After aligning, you subtract just like you would with whole numbers, starting from the rightmost digit.

Step-by-Step: Subtracting Decimals

1. Step 1: Write the numbers — Write the larger number (minuend) above the smaller number (subtrahend). Make sure to align their decimal points exactly one below the other.
2. Step 2: Add trailing zeros (if needed) — If the numbers have a different number of decimal places, add zeros to the end of the number with fewer decimal places until both numbers have the same number of decimal places. This doesn't change the value of the number.
3. Step 3: Subtract from right to left — Start subtracting the digits from the rightmost column, just like you do with whole numbers. If a digit in the top number is smaller than the digit below it, you'll need to borrow from the digit to its left.
4. Step 4: Place the decimal point — Once you've subtracted all the digits, place the decimal point in your answer (the difference) directly below the decimal points in the numbers above. The decimal point in the answer will be in the same column as the decimal points in the numbers being subtracted.

Worked Examples of Decimal Subtraction

• Example 1: Subtract 35.74 from 60.00 60.00 - 35.74 ------- 24.26 Explanation: We align the decimal points. Since 60 is a whole number, we write it as 60.00 to match the two decimal places of 35.74. Then we subtract column by column, borrowing when necessary.
• Example 2: Find the difference between 18.5 and 6.79 18.50 (Add a zero to 18.5 to match decimal places) - 6.79 -------- 11.71 Explanation: We add a zero to 18.5 to make it 18.50, aligning the hundredths place. Then, we subtract from right to left, borrowing from the left when a digit is smaller.
• Example 3: Subtract 0.9 from 1.00 1.00 - 0.90 (Add a zero to 0.9) ------- 0.10 Explanation: Convert 0.9 to 0.90 to have the same number of decimal places as 1.00. Then proceed with standard subtraction.

Exam Tip: Avoiding Common Mistakes in Decimal Subtraction

Many students make small but significant errors when subtracting decimals. Here are the most common ones and how to avoid them:

1. Not aligning decimal points: This is the biggest mistake! Always write the numbers one below the other, making sure the decimal points are perfectly vertical. If you don't, you'll be subtracting tenths from hundredths, leading to a wrong answer.

1. Forgetting to add trailing zeros: When numbers have different decimal places (e.g., 5.3 - 2.15), remember to write 5.3 as 5.30. This helps maintain place value alignment and makes borrowing clearer.

1. Borrowing errors: Just like with whole numbers, be careful when borrowing. If you borrow from a zero, you might need to borrow from the next digit to its left first. Practice makes perfect here!

1. Misplacing the decimal point in the answer: The decimal point in your final answer should always be directly below the decimal points in the numbers you subtracted. Double-check its position before finalizing your answer.

Practice Questions with Solutions

• Q: Subtract ₹18.25 from ₹20.75. A: Step 1: Align the decimal points. 20.75 - 18.25 --------- Step 2: Subtract from right to left. 5 - 5 = 0 7 - 2 = 5 0 - 8 (borrow from 2 to make 10, 2 becomes 1) = 2 1 - 1 = 0 Step 3: Place the decimal point. The decimal point is placed after the second digit from the right. Final answer: ₹2.50
• Q: Find the value of 5.0 - 2.34. A: Step 1: Align the decimal points and add trailing zeros to 5.0 to make it 5.00. 5.00 - 2.34 --------- Step 2: Subtract from right to left, borrowing as needed. 0 - 4 (borrow from 0, then from 5) -> 10 - 4 = 6 9 - 3 = 6 (after borrowing from the first 0, it became 9) 4 - 2 = 2 (after 5 lent to the 0, it became 4) Step 3: Place the decimal point. Final answer: 2.66
• Q: Rahul bought 4.5 kg of apples and 2.150 kg of mangoes. How much more do the apples weigh than the mangoes? A: Step 1: Identify the given weights and the operation needed. Weight of apples = 4.5 kg Weight of mangoes = 2.150 kg We need to find the difference, so we subtract. Step 2: Align decimal points and add trailing zeros. 4.500 - 2.150 --------- Step 3: Subtract from right to left. 0 - 0 = 0 0 - 5 (borrow from 5) -> 10 - 5 = 5 4 - 1 = 3 (after 5 lent to 0, it became 4) 4 - 2 = 2 Step 4: Place the decimal point. Final answer: Apples weigh 2.350 kg more than mangoes.
• Q: Subtract 11.6 from 13.98. A: Step 1: Align decimal points and add trailing zeros. 13.98 - 11.60 (Add a zero to 11.6) --------- Step 2: Subtract from right to left. 8 - 0 = 8 9 - 6 = 3 3 - 1 = 2 1 - 1 = 0 Step 3: Place the decimal point. Final answer: 2.38

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