CBSE Class 6 Maths: Knowing Our Numbers - Exercise 1.3 (Estimation)

What is Estimation and Rounding Off?

Estimation means finding a value that is close enough to the actual answer, rather than the exact answer. It's like making a good guess that is still reasonable. For example, if you have ₹48 and want to buy something that costs ₹23, you might quickly think "about ₹50 and ₹20," which helps you estimate if you have enough money without needing to calculate the precise total. Estimation is vital for quick mental math and checking if an exact calculation makes sense.

Rounding off is the main technique we use for estimation. It involves simplifying a number by replacing some digits with zeros, based on a specific place value (like tens, hundreds, or thousands). When we round off, we make a number simpler to work with while keeping it close to its original value. For instance, rounding 47 to the nearest ten gives 50, and rounding 42 to the nearest ten gives 40. The goal is to get to the 'nearest' friendly number that ends in zeros. This makes addition, subtraction, and multiplication much easier to perform mentally or quickly on paper.

Key Definitions

Estimation

Finding an approximate value or a rough calculation of a quantity or value, rather than an exact one. It helps in making quick decisions and checking the reasonableness of answers.

Rounding Off

A method of approximating a number to a specific place value (like nearest 10, 100, or 1000) by replacing digits to its right with zeros, making the number simpler to use.

Steps to Round Off Numbers

1. Rounding to the Nearest 10 — To round a number to the nearest 10, look at the digit in the ones place. If the ones digit is 0, 1, 2, 3, or 4 (less than 5), we round down. This means we keep the tens digit as it is and change the ones digit to 0. Example: 73 rounds down to 70. If the ones digit is 5, 6, 7, 8, or 9 (5 or more), we round up. This means we increase the tens digit by 1 and change the ones digit to 0. Example: 78 rounds up to 80.
2. Rounding to the Nearest 100 — To round a number to the nearest 100, look at the digit in the tens place. If the tens digit is 0, 1, 2, 3, or 4 (less than 50, considering the ones digit), we round down. Keep the hundreds digit as it is and change the tens and ones digits to 0. Example: 432 rounds down to 400. If the tens digit is 5, 6, 7, 8, or 9 (50 or more, considering the ones digit), we round up. Increase the hundreds digit by 1 and change the tens and ones digits to 0. Example: 478 rounds up to 500.
3. Rounding to the Nearest 1000 — To round a number to the nearest 1000, look at the digit in the hundreds place. If the hundreds digit is 0, 1, 2, 3, or 4 (less than 500, considering tens and ones digits), we round down. Keep the thousands digit as it is and change the hundreds, tens, and ones digits to 0. Example: 5234 rounds down to 5000. If the hundreds digit is 5, 6, 7, 8, or 9 (500 or more, considering tens and ones digits), we round up. Increase the thousands digit by 1 and change the hundreds, tens, and ones digits to 0. Example: 5789 rounds up to 6000.

Estimating Sums, Differences, and Products

• Example 1: Estimate the sum of 347 and 582 by rounding to the nearest hundred. Step 1: Round 347 to the nearest hundred. The tens digit is 4, which is less than 5, so we round down. 347 rounds to 300. Step 2: Round 582 to the nearest hundred. The tens digit is 8, which is 5 or more, so we round up. 582 rounds to 600. Step 3: Add the rounded numbers. 300 + 600 = 900. Final answer: The estimated sum is 900.
• Example 2: Estimate the difference between 821 and 295 by rounding to the nearest ten. Step 1: Round 821 to the nearest ten. The ones digit is 1, which is less than 5, so we round down. 821 rounds to 820. Step 2: Round 295 to the nearest ten. The ones digit is 5, which is 5 or more, so we round up. 295 rounds to 300. Step 3: Subtract the rounded numbers. 820 - 300 = 520. Final answer: The estimated difference is 520.
• Example 3: Estimate the product of 17 and 32 by rounding to the nearest ten. Step 1: Round 17 to the nearest ten. The ones digit is 7, which is 5 or more, so we round up. 17 rounds to 20. Step 2: Round 32 to the nearest ten. The ones digit is 2, which is less than 5, so we round down. 32 rounds to 30. Step 3: Multiply the rounded numbers. 20 x 30 = 600. Final answer: The estimated product is 600.

Exam Tip: Avoiding Common Mistakes in Rounding

One of the most frequent mistakes students make is looking at the wrong digit when rounding. Remember:

• For rounding to the nearest 10, always look at the ones digit.
• For rounding to the nearest 100, always look at the tens digit.
• For rounding to the nearest 1000, always look at the hundreds digit.

Another common error is forgetting to change all digits to the right of the rounding place to zero. For instance, if you round 347 to the nearest hundred, it becomes 300, not just 3. Also, be careful with the '5' rule: if the deciding digit is 5 or greater, you always round up!

Practice Questions with Solutions

• Q: Estimate the sum of 432 and 187 by rounding to the nearest hundred. A: Step 1: Round 432 to the nearest hundred. The tens digit is 3, so round down to 400. Step 2: Round 187 to the nearest hundred. The tens digit is 8, so round up to 200. Step 3: Add the rounded numbers: 400 + 200 = 600. Final answer: The estimated sum is 600.
• Q: Estimate the difference between 765 and 312 by rounding to the nearest ten. A: Step 1: Round 765 to the nearest ten. The ones digit is 5, so round up to 770. Step 2: Round 312 to the nearest ten. The ones digit is 2, so round down to 310. Step 3: Subtract the rounded numbers: 770 - 310 = 460. Final answer: The estimated difference is 460.
• Q: Give a rough estimate (by rounding off to nearest hundreds) and also a closer estimate (by rounding off to nearest tens): 5290 + 17986. A: Rough estimate (nearest hundreds): Step 1: Round 5290 to the nearest hundred. The tens digit is 9, so round up to 5300. Step 2: Round 17986 to the nearest hundred. The tens digit is 8, so round up to 18000. Step 3: Add: 5300 + 18000 = 23300. Closer estimate (nearest tens): Step 1: Round 5290 to the nearest ten. The ones digit is 0, so keep as 5290. Step 2: Round 17986 to the nearest ten. The ones digit is 6, so round up to 17990. Step 3: Add: 5290 + 17990 = 23280. Final answer: Rough estimate is 23300, closer estimate is 23280.
• Q: Estimate the product of 28 and 71 by rounding to the nearest ten. A: Step 1: Round 28 to the nearest ten. The ones digit is 8, so round up to 30. Step 2: Round 71 to the nearest ten. The ones digit is 1, so round down to 70. Step 3: Multiply the rounded numbers: 30 x 70 = 2100. Final answer: The estimated product is 2100.

Frequently Asked Questions