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Number System - Estimation and Rounding off

Grade 4ICSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Meaning of Estimation: Estimation is a way of finding a number that is close enough to the right answer, often called a 'rough guess'. It is used to make calculations simpler and quicker. For example, if a bag contains 4848 marbles, we can estimate it as 'about 5050'.

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Rounding to the Nearest 1010: To round a number to the nearest 1010, look at the digit in the ones place. If the ones digit is 55 or greater (5,6,7,8,95, 6, 7, 8, 9), round up by adding 11 to the tens digit and changing ones to 00. If the ones digit is less than 55 (0,1,2,3,40, 1, 2, 3, 4), round down by keeping the tens digit the same and changing ones to 00. Imagine a number line where 2323 is closer to 2020, while 2727 is closer to 3030.

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Rounding to the Nearest 100100: To round to the nearest 100100, look at the digit in the tens place. If the tens digit is 55 or more, increase the hundreds digit by 11 and make tens and ones places 00. If the tens digit is less than 55, keep the hundreds digit the same and change both tens and ones to 00. Visually, on a scale of 100100 to 200200, the midpoint is 150150; any number from 150150 onwards moves to 200200.

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Rounding to the Nearest 10001000: Observe the digit in the hundreds place. If the hundreds digit is 5,6,7,8,5, 6, 7, 8, or 99, round up by adding 11 to the thousands digit. If it is 0,1,2,3,0, 1, 2, 3, or 44, keep the thousands digit as it is. All digits to the right (hundreds, tens, ones) become 00. For example, 4,3204,320 rounds to 4,0004,000 because 33 is less than 55.

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The Hill Method (Visual Concept): Imagine a hill with numbers 0,1,2,3,40, 1, 2, 3, 4 on the left slope and 5,6,7,8,95, 6, 7, 8, 9 on the right slope. If a ball is on the 1,2,3,1, 2, 3, or 44 mark, it rolls back down to the current place value (rounding down). If it reaches the 55 mark or higher, it rolls forward to the next higher place value (rounding up).

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Estimating Sums and Differences: To estimate the result of addition or subtraction, round each number to the same place value (like the nearest 1010 or 100100) first, and then perform the operation. For example, 58+2158 + 21 can be estimated as 60+20=8060 + 20 = 80.

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Estimating Products: To estimate a product, round the factors to their greatest place value. For a 22-digit number, round to the nearest 1010. For a 33-digit number, round to the nearest 100100. Then multiply the rounded numbers. Example: 22×48≈20×50=1,00022 \times 48 \approx 20 \times 50 = 1,000.

📐Formulae

RoundingUp:Target Digit+1 (if neighbor ≥5)Rounding Up: \text{Target Digit} + 1 \text{ (if neighbor } \ge 5)

RoundingDown:Target Digit stays same (if neighbor <5)Rounding Down: \text{Target Digit stays same (if neighbor } < 5)

EstimatedSum≈Round(a)+Round(b)Estimated Sum \approx Round(a) + Round(b)

EstimatedDifference≈Round(a)−Round(b)Estimated Difference \approx Round(a) - Round(b)

EstimatedProduct≈Round(a)×Round(b)Estimated Product \approx Round(a) \times Round(b)

💡Examples

Problem 1:

Round 6,7486,748 to the nearest 100100.

Solution:

Step 1: Identify the digit in the hundreds place, which is 77. \ Step 2: Look at the digit to its right (the tens place), which is 44. \ Step 3: Since 4<54 < 5, we round down. \ Step 4: Keep the hundreds digit 77 as it is and change the digits in the tens and ones places to 00. \ Result: 6,7006,700.

Explanation:

To round to the nearest hundred, the tens digit determines whether the hundreds digit increases or stays the same.

Problem 2:

Estimate the sum of 436436 and 281281 by rounding to the nearest 100100.

Solution:

Step 1: Round 436436 to the nearest 100100. The tens digit is 33 (3<53 < 5), so 436≈400436 \approx 400. \ Step 2: Round 281281 to the nearest 100100. The tens digit is 88 (8>58 > 5), so 281≈300281 \approx 300. \ Step 3: Add the rounded numbers: 400+300=700400 + 300 = 700. \ Final estimated sum: 700700.

Explanation:

Estimation is done by rounding each addend to the specified place value before adding.