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Number Play - Simple Estimation

Grade 6CBSE

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

🔑Concepts

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Estimation involves finding a number that is close enough to the right answer, usually to make calculations simpler. It is often done by rounding numbers.

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To round a number to the nearest 1010, look at the digit in the ones place. If the ones digit is 55 or more, round up; if it is less than 55, round down. For example, 6767 becomes 7070 and 6262 becomes 6060.

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To round a number to the nearest 100100, look at the digit in the tens place. If the tens digit is 55 or more, round up; if it is less than 55, round down. For example, 853853 becomes 900900 and 849849 becomes 800800.

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General Rule for Estimation: Round each number to its greatest place value. For example, in 439+334+4,317439 + 334 + 4,317, round the first two to the nearest hundred and the last to the nearest thousand.

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Estimating Products: Round each factor to its greatest place value. For example, to estimate 63×18263 \times 182, round 6363 to 6060 and 182182 to 200200 to get 60×200=12,00060 \times 200 = 12,000.

📐Formulae

Estimated Sum≈Round(a)+Round(b)Estimated\ Sum \approx Round(a) + Round(b) balances accuracy and ease of calculation.

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

💡Examples

Problem 1:

Estimate the sum: 5,290+17,9865,290 + 17,986 to the nearest thousand.

Solution:

5,000+18,000=23,0005,000 + 18,000 = 23,000

Explanation:

Rounding 5,2905,290 to the nearest thousand gives 5,0005,000 (since the hundreds digit 2<52 < 5). Rounding 17,98617,986 to the nearest thousand gives 18,00018,000 (since the hundreds digit 9≥59 \ge 5). The calculation is: 5000+1800023000\begin{array}{r} 5000 \\ +18000 \\ \hline 23000 \end{array}

Problem 2:

Estimate the difference: 5,673−4365,673 - 436 by rounding to the nearest hundred.

Solution:

5,700−400=5,3005,700 - 400 = 5,300

Explanation:

5,6735,673 rounded to the nearest hundred is 5,7005,700 because the tens digit is 77. 436436 rounded to the nearest hundred is 400400 because the tens digit is 33. The estimation is: 5700−4005300\begin{array}{r} 5700 \\ -400 \\ \hline 5300 \end{array}

Problem 3:

Estimate the product of 81×47981 \times 479 using the general rule.

Solution:

80×500=40,00080 \times 500 = 40,000

Explanation:

Using the general rule, we round each number to its greatest place. 8181 is rounded to the nearest ten (8080). 479479 is rounded to the nearest hundred (500500). The product is 80×500=40,00080 \times 500 = 40,000.