Numbers and operations · Ages 12–13
Approximation & estimation worksheet
Covers: Rounding off to a place value, Rounding to decimal places, Significant figures, Rounding up and rounding down, Estimation strategies, Estimating when shopping, Planning an estimate
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Approximation & estimation worksheet
Numbers and operations · Ages 12–13
Numsprite
numsprite.com
Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.8.6582 correct to 2 decimal places is .
Answer:
2.4,603 rounded up to the nearest hundred is .
Answer:
3.Round each number to the nearest hundred to estimate 548 + 512:
Answer:
Part B: Choose, or true or false (2 marks each)
4.1,468 correct to the nearest ten is 1,470.
True or false?
Answer:
5.The arrow points to a number. What is it to the nearest whole number?
- A. 9
- B. 9.7
- C. 10
- D. 9.5
Choose the right answer
Answer:
6.The arrow points to a number. What is it correct to 1 decimal place?
- A. 6.33
- B. 6.3
- C. 6.4
- D. 6.35
Choose the right answer
Answer:
7.0.000102 has 7 significant figures.
True or false?
Answer:
8.What is 0.002627 correct to 3 significant figures?
- A. 0.0026
- B. 0.003
- C. 0.00262
- D. 0.00263
Choose the right answer
Answer:
9.97.665 rounded up to 1 decimal place gives the same answer as rounded off to 1 decimal place.
True or false?
Answer:
10.Estimating 51 × 65 as 60 × 70 = 4,200, the exact value is less than 4,200.
True or false?
Answer:
11.You have $70 and want three things: $14.8, $9.6 and $27.3. To be sure, by estimating, that the money is enough, what should you do to each price?
- A. Round it down to the dollar
- B. Count only the dearest
- C. Round it up to the dollar
- D. Round it off to the dollar
Choose the right answer
Answer:
12.Working out 32 × 62 on a calculator, which result is sensible? Check with an estimate first.
- A. 1,984
- B. 198
- C. 94
- D. 19,840
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.An exhibition had 867,014 visits. The news gave the figure to the nearest thousand. What figure did it give?
Working:
Answer:
14.A city has 5,427,397 people. Correct to 2 significant figures, about how many is that?
Working:
Answer:
15.Tsz-hin is 10 years and 8 months old. Ages are rounded down, so Tsz-hin is 11.
True or false?
Working:
Answer:
16.5 people share $4,005 of prize money. Estimate with a compatible number: change 4,005 to the nearest whole hundred that 5 divides, , and each gets about dollars.
Fill in each blank
Working:
Answer:
17.An online shop delivers free from $400. With $245 of goods chosen, socks at $23 a pair are added. At least how many pairs?
Working:
Answer:
18.A wall is 8.8 m long and 4.1 m high, and a can of paint covers 10 square metres. Paint errs on the big side. At least how many cans?
Working:
Answer:
Show the answers and working
Approximation & estimation worksheet: Answers and working
Part A: Working out and filling in
1. 8.66
Look at the third decimal place, 8: 5 or more rounds up, otherwise it drops, and everything after goes. So 8.66.
2. 4,700
Rounding up: whatever follows the hundreds, however small, the hundreds go up by 1. So 4,700.
3. 1000
548 ≈ 500 and 512 ≈ 500, so 500 + 500 = 1,000.
Part B: Choose, or true or false
4. True
The ones digit is 8: 5 or more rounds up, 4 or less drops. So 1,470.
5. C. 10
The arrow is at 9.7, between 9 and 10. Look at the first decimal place: 5 or more rounds up, otherwise it drops. So 10.
6. B. 6.3
The arrow is at 6.33. Look at the second decimal place: 5 or more rounds up, otherwise it drops. So 6.3.
7. False
The 4 zeros in front of 0.000102 only place the point; they are not significant. So 3.
8. D. 0.00263
Count three figures from 2, the first digit that isn't 0, then look at the fourth, 7: it rounds up. So 0.00263.
9. True
Rounding up gives 97.7; the second decimal place is 6, so rounding off gives 97.7.
10. True
51 became 60 and 65 became 70: both bigger makes the estimate too big; both smaller, too small.
11. C. Round it up to the dollar
Rounded up, every price is too big, so the total, 53, is too big; if even that is within 70, the money is surely enough.
12. A. 1,984
32 × 62 ≈ 30 × 60 = 1,800; only 1,984 is near the estimate.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 867,000 visits
The hundreds digit after the thousands is 0: 5 or more rounds up, otherwise it drops, and the rest become 0. So 867,000.
14. 5,400,000 people
Count two significant figures, look at the third, and fill the rest with 0 to keep the place values: 5,400,000.
15. False
Ages round down: until the next birthday it is still 10, however many months have passed.
16. 4,000, 800
4,005 ≈ 4,000, and 4,000 ÷ 5 = 800.
17. 7 pairs
$155 short: 400 − 245 = 155, and 155 ÷ 23 rounded up is 7 pairs.
18. 4 cans
The area is 8.8 × 4.1 = 36.08 m²; 36.08 ÷ 10 rounded up is 4 cans.
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