Estimate the sum by rounding each number to 1 significant figure, then add your estimates.
(a)Estimate 18 750 + 4 220.(3)
3
Use 1 significant figure estimates to approximate each product. Round first, then multiply mentally.
(a)Estimate 1 780 x 2 450.(3)
4
Estimate the value of 0.372 + 0.045 using 1 significant figure then give an appropriate check by computing the exact sum and comparing.
(a)Estimate the sum to 1 s.f.(2)
(b)Calculate the exact sum and say whether the estimate was an overestimate or underestimate.(2)
5
A shop lists a jacket at 79.99 pounds and a scarf at 8.45 pounds. Use 1 significant figure estimates to decide whether a budget of 90 pounds is enough. Show your estimate and a check using the exact total.
(a)Estimate the two prices to 1 significant figure and give the estimated total.(2)
(b)Calculate the exact total and say whether 90 pounds is enough.(2)
6
Round each measurement to 1 significant figure to give an approximate distance.
(a)Round 3.8 km to 1 significant figure.(1)
(b)Round 0.67 km to 1 significant figure.(1)
Mark scheme · KS3.M-N14 Estimation and Checking
Question 1
(a) B1 4 000 cao
(a) Answer: 4000
(b) B1 0.05 cao
(b) Answer: 0.05
(c) B1 90 000 cao
(c) Answer: 90000
(d) B1 1.0 cao
(d) Answer: 1.0
Question 2
(a) M1 first number rounded to 1 s.f. correctly: 18 750 -> 20 000
(a) M1 second number rounded to 1 s.f. correctly: 4 220 -> 4 000
(a) A1 correct estimated total 24 000 cao
(a) Answer: 24000
Question 3
(a) M1 first number rounded to 1 s.f. correctly: 1 780 -> 2 000
(a) M1 second number rounded to 1 s.f. correctly: 2 450 -> 2 000
(a) A1 correct estimated product 4 000 000 cao
(a) Answer: 4000000
Question 4
(a) M1 both numbers rounded to 1 s.f. correctly, e.g. 0.372 -> 0.4 and 0.045 -> 0.05
(a) A1 a consistent estimate given from the rounded values, e.g. 0.4 + 0.05 = 0.45 cao
(a) Answer: 0.45
(b) M1 correct exact sum 0.417
(b) A1 correctly state whether estimate is an overestimate or underestimate (here 0.45 > 0.417 so overestimate) cao
(b) Answer: 0.417; overestimate
Question 5
(a) M1 both items rounded to 1 s.f. correctly: 79.99 -> 80 and 8.45 -> 8
(a) A1 correct estimated total 88 cao
(a) Answer: 80 and 8; estimate 88
(b) M1 correct exact total 88.44
(b) A1 state correctly that 90 pounds is enough cao