64
Estimating values
Textbook: Part 2, lesson 64, pp. 78–80
GoalEstimating values: lower and upper bounds of a sum.
New words
estimating · chamalashlower bound · quyi chegaraupper bound · yuqori chegaragross error · qo‘pol xato
Explanation
Estimating a result before calculating helps us catch gross errors. To estimate a sum we add round numbers smaller than each addend to get the lower bound, and round numbers larger than each addend to get the upper bound: for 263 + 538 we get 200 + 500 = 700 and 300 + 600 = 900, so 700 < 263 + 538 < 900. We can also estimate a sum by rounding: 3 874 + 2 126 ≈ 4 000 + 2 000 = 6 000.
Worked examples
263 + 538: lower bound 200 + 500 = 700, upper bound 300 + 600 = 900; the exact sum is 801.
31 480 + 14 260 < 40 000 + 20 000 = 60 000, so a total of 65 000 sum cannot be right.
Class activity
“Guess first”: before calculating write the lower and upper bounds of a sum, then calculate exactly and check it lies between them.
Practice
1
Find the lower bound of the sum 263 + 538 (200 + 500).
700
2
Find the upper bound of the sum 263 + 538 (300 + 600).
900
3
A family must pay 31 480 sum for gas and 14 260 sum for water. The cashier said the total is 65 000 sum. With the upper bound 40 000 + 20 000, was the cashier right?
No, the sum is less than 60 000
4
Estimate the sum 3 874 + 2 126 by rounding each number to thousands.
6000