Sec 1 Maths Approximation and estimation worksheet with answers

A free Sec 1 Maths worksheet on approximation and estimation: 8 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 1 Maths worksheet: Approximation and estimation

Total: 30 marksSuggested time: 45 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

(a)The distance between two MRT stations is

12.45

km, correct to 2 decimal places. Complete the statement: the actual distance is less than

\ldots\ldots

km.

Answer (a)km[1]

(b)The height of an HDB block is

60

m, correct to the nearest 10 m. Given that the actual height of the block is

h

m, write down the range of possible values of

h

Answer (b)[1]

(a)Write

1999

correct to 3 significant figures.

Answer (a)[1]

(b)Write

74\,962

correct to 3 significant figures.

Answer (b)[1]

By rounding each number to the nearest whole number, estimate the value of

\dfrac{8.14 \times 4.83}{4.86}

. Show your working clearly.

Answer[2]

(a)Write

8952

correct to the nearest 100.

Answer (a)[1]

(b)Use a calculator to evaluate

\sqrt{50}

, giving your answer correct to 1 decimal place.

Answer (b)[1]

(a)Write

3.14159

correct to 2 decimal places.

Answer (a)[1]

(b)Use a calculator to evaluate

\dfrac{2.4^{3} - \sqrt{30}}{1.3 \times 2.75}

, giving your answer correct to 3 significant figures.

Answer (b)[2]

Section B

(a)(i)The mass of a parcel is

1200

g, correct to the nearest 100 g. Complete the statement: the actual mass of the parcel is less than

\ldots\ldots

Answer (a)(i)g[1]

(a)(ii)The length of a rod is

150

cm, correct to the nearest 10 cm. Given that the actual length of the rod is

l

cm, write down the range of possible values of

l

Answer (a)(ii)[1]

(b)(i)By writing each number correct to 1 significant figure, estimate the value of

\dfrac{19.8 \times 2.96}{0.0612}

Answer (b)(i)[2]

(b)(ii)Nur Aisyah estimates the value of

\dfrac{396}{0.214}

by writing each number correct to 1 significant figure. Without finding the exact value, explain whether the estimate is greater than or less than the exact value.

Answer (b)(ii)[1]

(a)Mei Ling uses a calculator and obtains

2.83 \times 0.618 = 17.4894

. By writing each number correct to 1 significant figure, state whether this answer is reasonable.

Answer (a)[2]

(b)(i)The time taken by a runner to complete a race is

13.84

s, correct to 2 decimal places. Given that the actual time taken is

t

s, write down the range of possible values of

t

Answer (b)(i)[1]

(b)(ii)The number of books in a library is

17\,080

, correct to 4 significant figures. Find the smallest and the largest possible number of books.

Answer (b)(ii)[3]

(a)(i)Write

8.204

correct to 2 significant figures.

Answer (a)(i)[1]

(a)(ii)Write

2.718

correct to 2 significant figures.

Answer (a)(ii)[1]

(b)(i)The number of books in a library is

45\,700

, correct to 3 significant figures. Find the smallest and the largest possible number of books.

Answer (b)(i)[3]

(b)(ii)The population of a town is

41\,250

, correct to 4 significant figures. Find the smallest and the largest possible population.

Answer (b)(ii)[3]

END OF PAPER

Answers and worked solutions

Question 1

(a)Answer:

12.45 + 0.005 = 12.455

km[1]

Half of

0.01

= 0.005

12.45 + 0.005 = 12.455

(b)Answer:

55 \leq h < 65

[1]

Half of

10

= 5

55 \leq h < 65

Question 2

(a)Answer:

1999 = 2000

(3 s.f.)[1]

The 4th significant figure is

9

.It is 5 or more, so round up.

1999 = 2000

(3 s.f.)

(b)Answer:

74\,962 = 75\,000

(3 s.f.)[1]

The 4th significant figure is

6

.It is 5 or more, so round up.

74\,962 = 75\,000

(3 s.f.)

Question 3

Answer:

= 8

[2]

\dfrac{8.14 \times 4.83}{4.86} \approx \dfrac{8 \times 5}{5}

= \dfrac{40}{5}

= 8

Question 4

(a)Answer:

8952 = 9000

(nearest 100)[1]

The deciding digit is

5

.It is 5 or more, so round up.

8952 = 9000

(nearest 100)

(b)Answer:

= 7.1

(1 d.p.)[1]

\sqrt{50} = 7.07106\ldots

= 7.1

(1 d.p.)

Question 5

(a)Answer:

3.14159 = 3.14

(2 d.p.)[1]

The deciding digit is

1

.It is 4 or less, so round down.

3.14159 = 3.14

(2 d.p.)

(b)Answer:

= 2.33

(3 s.f.)[2]

2.4^{3} - \sqrt{30} = 8.3467\ldots

1.3 \times 2.75 = 3.575

\dfrac{8.3467\ldots}{3.575} = 2.3347\ldots

= 2.33

(3 s.f.)

Question 6

(a)(i)Answer:

1200 + 50 = 1250

g[1]

Half of

100

= 50

1200 + 50 = 1250

(a)(ii)Answer:

145 \leq l < 155

[1]

Half of

10

= 5

145 \leq l < 155

(b)(i)Answer:

= 1000

[2]

\dfrac{19.8 \times 2.96}{0.0612} \approx \dfrac{20 \times 3}{0.06}

= \dfrac{60}{0.06}

= 1000

(b)(ii)Answer: OVER[1]

396 \rightarrow 400

is rounded up;

0.214 \rightarrow 0.2

is rounded down.The top was rounded up and the bottom down, so the estimate is greater than the exact value.

Question 7

(a)Answer: NO[2]

2.83 \times 0.618 \approx 3 \times 0.6

= 1.8

17.4894

is about 10 times the estimate

1.8

, so the answer is not reasonable: the decimal point is in the wrong place.

(b)(i)Answer:

13.835 \leq t < 13.845

[1]

Half of

0.01

= 0.005

13.835 \leq t < 13.845

(b)(ii)Answer:

\phantom{\text{Largest}} = 17084

(

17085

itself rounds up to

17090

).[3]

17\,080

to 4 significant figures is rounded to the nearest

10

.Half of

10

5

\text{Smallest} = 17080 - 5

\phantom{\text{Smallest}} = 17075

\text{Largest} = 17080 + 5 - 1

\phantom{\text{Largest}} = 17084

(

17085

itself rounds up to

17090

Question 8

(a)(i)Answer:

8.204 = 8.2

(2 s.f.)[1]

The 3rd significant figure is

0

.It is 4 or less, so round down.

8.204 = 8.2

(2 s.f.)

(a)(ii)Answer:

2.718 = 2.7

(2 s.f.)[1]

The 3rd significant figure is

1

.It is 4 or less, so round down.

2.718 = 2.7

(2 s.f.)

(b)(i)Answer:

\phantom{\text{Largest}} = 45749

(

45750

itself rounds up to

45800

).[3]

45\,700

to 3 significant figures is rounded to the nearest

100

.Half of

100

50

\text{Smallest} = 45700 - 50

\phantom{\text{Smallest}} = 45650

\text{Largest} = 45700 + 50 - 1

\phantom{\text{Largest}} = 45749

(

45750

itself rounds up to

45800

(b)(ii)Answer:

\phantom{\text{Largest}} = 41254

(

41255

itself rounds up to

41260

).[3]

41\,250

to 4 significant figures is rounded to the nearest

10

.Half of

10

5

\text{Smallest} = 41250 - 5

\phantom{\text{Smallest}} = 41245

\text{Largest} = 41250 + 5 - 1

\phantom{\text{Largest}} = 41254

(

41255

itself rounds up to

41260

Practice questions by skill

Sec 1 Maths Approximation and estimation worksheet with answers

In the print window, choose Save as PDF to download it.

Need the formulas first? Read the Approximation and estimation notes. Or practise it online with step-by-step help when you get one wrong.

Section A

(a)The distance between two MRT stations is

12.45

km, correct to 2 decimal places. Complete the statement: the actual distance is less than

\ldots\ldots

km.

Answer (a)km[1]

(b)The height of an HDB block is

60

m, correct to the nearest 10 m. Given that the actual height of the block is

h

m, write down the range of possible values of

h

Answer (b)[1]

Section B

(a)(i)The mass of a parcel is

1200

g, correct to the nearest 100 g. Complete the statement: the actual mass of the parcel is less than

\ldots\ldots

Answer (a)(i)g[1]

(a)(ii)The length of a rod is

150

cm, correct to the nearest 10 cm. Given that the actual length of the rod is

l

cm, write down the range of possible values of

l

Answer (a)(ii)[1]

(b)(i)By writing each number correct to 1 significant figure, estimate the value of

\dfrac{19.8 \times 2.96}{0.0612}

Answer (b)(i)[2]

(b)(ii)Nur Aisyah estimates the value of

\dfrac{396}{0.214}

by writing each number correct to 1 significant figure. Without finding the exact value, explain whether the estimate is greater than or less than the exact value.

Answer (b)(ii)[1]

Answers and worked solutions

Question 1

(a)Answer:

12.45 + 0.005 = 12.455

km[1]

Half of

0.01

= 0.005

12.45 + 0.005 = 12.455

(b)Answer:

55 \leq h < 65

[1]

Half of

10

= 5

55 \leq h < 65

Question 2

(a)Answer:

1999 = 2000

(3 s.f.)[1]

The 4th significant figure is

9

.It is 5 or more, so round up.

1999 = 2000

(3 s.f.)

(b)Answer:

74\,962 = 75\,000

(3 s.f.)[1]

The 4th significant figure is

6

.It is 5 or more, so round up.

74\,962 = 75\,000

(3 s.f.)

Question 3

Answer:

= 8

[2]

\dfrac{8.14 \times 4.83}{4.86} \approx \dfrac{8 \times 5}{5}

= \dfrac{40}{5}

= 8

Question 4

(a)Answer:

8952 = 9000

(nearest 100)[1]

The deciding digit is

5

.It is 5 or more, so round up.

8952 = 9000

(nearest 100)

(b)Answer:

= 7.1

(1 d.p.)[1]

\sqrt{50} = 7.07106\ldots

= 7.1

(1 d.p.)

Question 5

(a)Answer:

3.14159 = 3.14

(2 d.p.)[1]

The deciding digit is

1

.It is 4 or less, so round down.

3.14159 = 3.14

(2 d.p.)

(b)Answer:

= 2.33

(3 s.f.)[2]

2.4^{3} - \sqrt{30} = 8.3467\ldots

1.3 \times 2.75 = 3.575

\dfrac{8.3467\ldots}{3.575} = 2.3347\ldots

= 2.33

(3 s.f.)

Question 6

(a)(i)Answer:

1200 + 50 = 1250

g[1]

Half of

100

= 50

1200 + 50 = 1250

(a)(ii)Answer:

145 \leq l < 155

[1]

Half of

10

= 5

145 \leq l < 155

(b)(i)Answer:

= 1000

[2]

\dfrac{19.8 \times 2.96}{0.0612} \approx \dfrac{20 \times 3}{0.06}

= \dfrac{60}{0.06}

= 1000

(b)(ii)Answer: OVER[1]

396 \rightarrow 400

is rounded up;

0.214 \rightarrow 0.2

is rounded down.The top was rounded up and the bottom down, so the estimate is greater than the exact value.

Question 7

(a)Answer: NO[2]

2.83 \times 0.618 \approx 3 \times 0.6

= 1.8

17.4894

is about 10 times the estimate

1.8

, so the answer is not reasonable: the decimal point is in the wrong place.

(b)(i)Answer:

13.835 \leq t < 13.845

[1]

Half of

0.01

= 0.005

13.835 \leq t < 13.845

(b)(ii)Answer:

\phantom{\text{Largest}} = 17084

(

17085

itself rounds up to

17090

).[3]

17\,080

to 4 significant figures is rounded to the nearest

10

.Half of

10

5

\text{Smallest} = 17080 - 5

\phantom{\text{Smallest}} = 17075

\text{Largest} = 17080 + 5 - 1

\phantom{\text{Largest}} = 17084

(

17085

itself rounds up to

17090

Question 8

(a)(i)Answer:

8.204 = 8.2

(2 s.f.)[1]

The 3rd significant figure is

0

.It is 4 or less, so round down.

8.204 = 8.2

(2 s.f.)

(a)(ii)Answer:

2.718 = 2.7

(2 s.f.)[1]

The 3rd significant figure is

1

.It is 4 or less, so round down.

2.718 = 2.7

(2 s.f.)

(b)(i)Answer:

\phantom{\text{Largest}} = 45749

(

45750

itself rounds up to

45800

).[3]

45\,700

to 3 significant figures is rounded to the nearest

100

.Half of

100

50

\text{Smallest} = 45700 - 50

\phantom{\text{Smallest}} = 45650

\text{Largest} = 45700 + 50 - 1

\phantom{\text{Largest}} = 45749

(

45750

itself rounds up to

45800

(b)(ii)Answer:

\phantom{\text{Largest}} = 41254

(

41255

itself rounds up to

41260

).[3]

41\,250

to 4 significant figures is rounded to the nearest

10

.Half of

10

5

\text{Smallest} = 41250 - 5

\phantom{\text{Smallest}} = 41245

\text{Largest} = 41250 + 5 - 1

\phantom{\text{Largest}} = 41254

(

41255

itself rounds up to

41260