Estimation
ICSE Class 6 · Mathematics · Chapter 2
What this chapter covers
- What estimation means
- Rounding off numbers
- Approximation of large numbers
- Estimating sums and differences
- Estimating products and quotients
Key points
- Estimation is finding a value close enough to the exact answer to be useful.
- Rounding off replaces a number by a nearby, simpler number ending in zeros.
- To round to any place, look at the digit just to its right: 0 to 4 rounds down, 5 to 9 rounds up.
- Every digit to the right of the rounding place becomes 0. Round in one step, never in stages.
- Large numbers can be approximated to the nearest ten thousand, lakh, ten lakh or crore. The sign ≈ means "is approximately equal to".
- To estimate a sum or difference, round each number, then add or subtract.
- To estimate a product, round each number to its greatest place, then multiply.
- To estimate a quotient, use nearby compatible numbers that divide easily.
- An estimate helps you check whether an exact answer is sensible.
Questions answered
What is an estimate? Give one example from your daily life.
An estimate is a quick, sensible value that is close to the exact one. Example: saying a bus journey takes "about one hour".
Round off 2,374 to the nearest ten, the nearest hundred and the nearest thousand.
Nearest ten: 2,370. Nearest hundred: 2,400. Nearest thousand: 2,000.
Round off 995 to the nearest ten.
The ones digit is 5, so round up. The 9 tens become 10 tens, which make a hundred. The answer is 1,000.
Round off 3,48,59,210 to the nearest lakh and to the nearest crore.
Nearest lakh: the ten thousands digit is 5, so round up to 3,49,00,000. Nearest crore: the ten lakhs digit is 4, so round down to 3,00,00,000.
Estimate 687 + 214 by rounding each number to the nearest hundred. Then find the exact sum.
700 + 200 = 900. The exact sum is 901.
Estimate 9,126 - 3,874 by rounding to the nearest thousand.
9,000 - 4,000 = 5,000. The exact difference is 5,252.
Estimate 73 × 58 by rounding each number to its greatest place.
70 × 60 = 4,200. The exact product is 4,234.
A farmer packs 2,416 mangoes into boxes of 12. Estimate the number of boxes he needs.
Use the compatible numbers 2,400 and 12: 2,400 ÷ 12 = 200. He needs about 200 boxes. The exact answer is 201 full boxes with 4 mangoes left over, so he needs 202 boxes.