Estimate 6830 + 2145 by rounding each number to 1 significant figure, then adding your estimates.
(2)
10
Estimate 3150 x 410 by rounding each number to 1 significant figure.
(2)
11
Estimate 78600 - 19700 by rounding each number to 1 significant figure.
(2)
12
Estimate 0.68 x 0.031 by rounding each number to 1 significant figure.
(2)
13
The exact value of 61 x 19 is 1159. Round each number to 1 significant figure to estimate the product, then state whether your estimate is an overestimate or an underestimate.
(2)
14
Round 12650 to 1 significant figure, then state whether the rounded value is greater than or less than the exact value.
(2)
15
Cinema tickets cost 8.95 pounds each. Estimate the total cost of 42 tickets by rounding each number to 1 significant figure, then calculate the exact cost and state whether it is more or less than your estimate.
(3)
16
A school books 3 coaches at 495 pounds each. Estimate the total cost by rounding 495 to 1 significant figure, then compare your estimate with the exact total cost of 1485 pounds. State whether the estimate is an overestimate or an underestimate.
(3)
17
Estimate 812 divided by 39 by rounding each number to 1 significant figure.
(3)
18
A rectangular room measures 3.8 m by 6.4 m. Estimate its area by rounding each measurement to 1 significant figure, then compare your estimate with the exact area of 24.32 m2. State whether the estimate is an overestimate or an underestimate.
(3)
19
A charity's till roll shows three donations: 1205.75 pounds, 640.20 pounds and 640.55 pounds.
(a)Use 1 significant figure estimates for each amount to estimate the total.(2)
(b)The exact total is 2486.50 pounds. State, with a reason, whether the exact total is greater or less than your estimate.(2)
20
A delivery contains four boxes weighing 187 kg, 92 kg, 348 kg and 63 kg.
(a)Find a 1 significant figure estimate for the total mass.(2)
(b)Calculate the exact total mass and state whether the estimate is an overestimate or an underestimate.(2)
Mark scheme · KS3.M-N14D Estimation and Checking: Fluency and Exam Drill
Question 1
B1 4000 cao
Answer: 4000
Question 2
B1 0.04 cao
Answer: 0.04
Question 3
B1 70000 cao
Answer: 70000
Question 4
B1 0.008 cao
Answer: 0.008
Question 5
B1 7 cao
Answer: 7
Question 6
B1 200 cao
Answer: 200
Question 7
B1 0.5 cao
Answer: 0.5
Question 8
B1 900000 cao
Answer: 900000
Question 9
M1 both numbers rounded to 1 s.f. correctly: 6830 -> 7000 and 2145 -> 2000
A1 correct estimated total 9000 cao
Answer: 9000
Question 10
M1 both numbers rounded to 1 s.f. correctly: 3150 -> 3000 and 410 -> 400
A1 correct estimated product 1200000 cao
Answer: 1200000
Question 11
M1 both numbers rounded to 1 s.f. correctly: 78600 -> 80000 and 19700 -> 20000
A1 correct estimated difference 60000 cao
Answer: 60000
Question 12
M1 both numbers rounded to 1 s.f. correctly: 0.68 -> 0.7 and 0.031 -> 0.03
A1 correct estimated product 0.021 cao
Answer: 0.021
Question 13
M1 correct estimate using 1 s.f. values: 60 x 20 = 1200
A1 correctly state overestimate, since 1200 > 1159 cao
Answer: 1200; overestimate
Question 14
M1 correct rounding to 1 s.f.: 12650 -> 10000
A1 correctly state that the rounded value (10000) is less than the exact value (12650) cao
Answer: 10000; the rounded value is less than the exact value
Question 15
M1 correct estimate using 1 s.f. values: 9 x 40 = 360
M1 correct exact calculation: 8.95 x 42 = 375.90
A1 correctly state the exact cost is more than the estimate, since 375.90 > 360 cao
Answer: Estimate 360; exact 375.90; the exact cost is more than the estimate
Question 16
M1 round 495 to 1 s.f. correctly: 495 -> 500
M1 correct estimated total: 3 x 500 = 1500
A1 correctly state overestimate, since 1500 > 1485 cao
Answer: Estimate 1500; overestimate
Question 17
M1 round 812 to 1 s.f. correctly: 812 -> 800
M1 round 39 to 1 s.f. correctly and set up the division: 39 -> 40, 800 / 40
A1 correct estimate 20 cao
Answer: 20
Question 18
M1 both measurements rounded to 1 s.f. correctly: 3.8 -> 4 and 6.4 -> 6
M1 correct estimated area: 4 x 6 = 24
A1 correctly state underestimate, since 24 < 24.32 cao
Answer: Estimate 24 m2; underestimate
Question 19
(a) M1 all three amounts rounded to 1 s.f. correctly: 1205.75 -> 1000, 640.20 -> 600, 640.55 -> 600
(a) A1 correct estimated total 2200 cao
(a) Answer: 2200
(b) M1 recognise every amount was rounded down to reach the estimate
(b) A1 correctly state the exact total (2486.50) is greater than the estimate (2200), because each amount was rounded down cao
(b) Answer: Greater than the estimate, because every amount was rounded down
Question 20
(a) M1 all four masses rounded to 1 s.f. correctly: 187 -> 200, 92 -> 90, 348 -> 300, 63 -> 60