Browse Rounding & bounds

56 questions at your level

DifficultyAllLevel 1Level 2Level 3Level 4Level 5

Rounding and significant figures

20 questions

LessonNot started
Round 38623862 to 1 significant figure.
●●●●●Level 11 markStart
Round 0.04720.0472 to 2 significant figures.
●●●●●Level 11 markStart
(a) Round 0.0047180.004718 to 2 significant figures. (1 mark)

(b) Round 0.0047180.004718 to 3 decimal places. (1 mark)
●●●●●Level 12 marksStart
Use your calculator to work out

19.6+2.738.4−3.15\dfrac{\sqrt{19.6} + 2.7^3}{8.4 - 3.15}
(a) Write down all the figures on your calculator display. (1 mark)
(b) Write your answer to part (a) correct to 3 significant figures. (1 mark)
●●●●●Level 12 marksStart
(a) Write 3.141593.14159 correct to 3 significant figures. [1]

(b) Write 0.067490.06749 correct to 2 significant figures. [1]
●●●●●Level 12 marksStart
Use your calculator to work out 7.32−2.921.6\dfrac{\sqrt{7.3^2 - 2.9^2}}{1.6}

Give your answer correct to 3 significant figures. [2]
●●●●●Level 12 marksStart
(a) Round 67 48367\,483 to 11 significant figure.

(b) Round 0.005680.00568 to 22 significant figures.

(c) Round 3.9963.996 to 22 decimal places.
●●●●●Level 23 marksStart
(a) Work out the value of

3.62+1.8412.7−4.36\frac{3.6^2 + 1.84}{\sqrt{12.7 - 4.36}}

Write down all the figures on your calculator display.

(2 marks)
(b) Work out the value of the reciprocal of 0.320.32

(1 mark)
●●●●●Level 23 marksStart
Use your calculator to work out

(4.9×cos⁡23∘)27.15−tan⁡64∘\frac{(4.9 \times \cos 23^\circ)^2}{7.15 - \tan 64^\circ}

Give your answer correct to 3 significant figures.

(2 marks)
●●●●●Level 22 marksStart
(a) Round 4562 to 2 significant figures.

(b) Round 0.030472 to 3 significant figures.

(c) Round 18.965 to 1 decimal place.
●●●●●Level 33 marksStart
x=5.3x = 5.3, correct to 1 decimal place. Write down the error interval for xx.
●●●●●Level 32 marksStart
The mass of a bag, mm kg, is 1212 kg correct to the nearest kilogram.

Write down the error interval for mm.
●●●●●Level 32 marksStart
A number, ww, is rounded to 22 significant figures.

The result is 0.460.46
(a) Write down the least possible value of ww.

(1 mark)

Marek says,

"The greatest possible value of ww is 0.46490.4649 because 0.4650.465 would round up to 0.470.47"
(b) Is Marek correct?

You must give a reason for your answer.

(1 mark)
●●●●●Level 32 marksStart
Ivan orders 587587 metres of fencing wire.

The wire costs £3.843.84 for every 1010 metres.
(a) Work out an estimate for the total cost of the wire.

(3 marks)
(b) Is your answer to part (a) an underestimate or an overestimate?

Give a reason for your answer.

(1 mark)
●●●●●Level 34 marksStart
The mass of a parcel is 340 g, correct to the nearest 10 g. Write down the error interval for the mass mm.
●●●●●Level 42 marksStart
A number yy is truncated to 1 decimal place. The result is 8.4. Write down the error interval for yy.
●●●●●Level 42 marksStart
The number of people at a concert is 2400, correct to the nearest 100.

(a) Write down the least possible number of people.

(b) Write down the greatest possible number of people.
●●●●●Level 42 marksStart
x=460x = 460, correct to 22 significant figures.

Write down the error interval for xx.
●●●●●Level 42 marksStart
A number yy is truncated to a whole number. The result is 2323.

Write down the error interval for yy.
●●●●●Level 42 marksStart
k=6.0k = 6.0, correct to 11 decimal place.

(a) Write down the error interval for kk.

(b) Maya says, "kk could be exactly 6.056.05." Explain why Maya is wrong.
●●●●●Level 53 marksStart

Estimation

15 questions

LessonNot started
Estimate the value of 48×2148 \times 21
●●●●●Level 12 marksStart
Estimate the value of 6122.9\dfrac{612}{2.9}
●●●●●Level 12 marksStart
Work out an estimate for 4.9×20.30.51\dfrac{4.9 \times 20.3}{0.51}

You must show your working. (2 marks)
●●●●●Level 12 marksStart
Work out an estimate for 7.9×3.220.48\dfrac{7.9 \times 3.2^2}{0.48}

You must show your working. [3]
●●●●●Level 23 marksStart
Work out an estimate for the value of 48.6×21.29.7\dfrac{48.6 \times 21.2}{9.7}

You must show your working.
●●●●●Level 33 marksStart
Work out an estimate for the value of 19.6×5.3\sqrt{19.6 \times 5.3}

You must show your working.
●●●●●Level 33 marksStart
Work out an estimate for the value of 39.2×5.19.8\dfrac{39.2 \times 5.1}{9.8}

You must show your working.
●●●●●Level 32 marksStart
Work out an estimate for the value of 6.8×3.1×4.96.8 \times 3.1 \times 4.9

You must show your working.
●●●●●Level 32 marksStart
Ivan orders 587587 metres of fencing wire.

The wire costs £3.843.84 for every 1010 metres.
(a) Work out an estimate for the total cost of the wire.

(3 marks)
(b) Is your answer to part (a) an underestimate or an overestimate?

Give a reason for your answer.

(1 mark)
●●●●●Level 34 marksStart
Work out an estimate for the value of 612×0.480.19\dfrac{612 \times 0.48}{0.19}

You must show your working.
●●●●●Level 43 marksStart
(a) Work out an estimate for 21% of 4130.

(b) Without further calculation, state whether your answer is an overestimate or an underestimate. Give a reason.
●●●●●Level 43 marksStart
Work out an estimate for the value of 5.860.021\dfrac{5.86}{0.021}

You must show your working.
●●●●●Level 42 marksStart
Tickets for a play cost £3.953.95 each.

A teacher buys 2828 tickets.

(a) Work out an estimate for the total cost.

(b) Without further calculation, state whether your estimate is an overestimate or an underestimate. Give a reason.
●●●●●Level 43 marksStart
A car travels 297 miles and uses 41.3 litres of fuel.

(a) Work out an estimate for the number of miles the car travels per litre.

(b) Is your estimate an overestimate or an underestimate? Give a reason.
●●●●●Level 53 marksStart
Work out an estimate for the value of 9.122×2.130.485\dfrac{9.12^2 \times 2.13}{0.485}

You must show your working.
●●●●●Level 53 marksStart

Upper and lower bounds

23 questions

LessonNot started
A length is 77 cm to the nearest centimetre. Write down the smallest possible length.
●●●●●Level 11 markStart
The height of a door is 198198 cm, correct to the nearest cm. Write down the upper bound of the height.
●●●●●Level 11 markStart
A bag of flour weighs 1.51.5 kg to the nearest 0.10.1 kg. Write down the error interval for the weight, ww kg.
●●●●●Level 22 marksStart
A number is 4040 to the nearest 1010. Write down the largest and smallest values it could be, using inequalities.
●●●●●Level 22 marksStart
The length of a shelf is 45 cm, correct to the nearest centimetre.

(a) Write down the lower bound of the length.

(b) Write down the upper bound of the length.
●●●●●Level 32 marksStart
The mass of a cat is 2.72.7 kg, correct to 11 decimal place.

(a) Write down the lower bound of the mass.

(b) Write down the upper bound of the mass.
●●●●●Level 32 marksStart
The side of a square is 5.45.4 cm, correct to 1 decimal place.

(a) Write down the error interval for the side length, ss cm. (2 marks)

(b) Work out the lower bound for the perimeter of the square. (1 mark)
●●●●●Level 33 marksStart
A rectangle has length 8.48.4 cm and width 5.65.6 cm, each measured correct to 1 decimal place.

Work out the upper bound for the area of the rectangle. (3 marks)
●●●●●Level 33 marksStart
x=7.36x = 7.36 correct to 2 decimal places. y=4.9y = 4.9 correct to 1 decimal place.

(a) Write down the error interval for yy. [2]

(b) Work out the upper bound of xy\dfrac{x}{y}. Give your answer correct to 3 significant figures. [3]
●●●●●Level 35 marksStart
A number, ww, is rounded to 22 significant figures.

The result is 0.460.46
(a) Write down the least possible value of ww.

(1 mark)

Marek says,

"The greatest possible value of ww is 0.46490.4649 because 0.4650.465 would round up to 0.470.47"
(b) Is Marek correct?

You must give a reason for your answer.

(1 mark)
●●●●●Level 32 marksStart
A rectangle measures 8.3 cm by 6.4 cm, each correct to 1 decimal place.8.3 cm6.4 cmDiagram NOT accurately drawn

Work out the upper bound of the area of the rectangle.
●●●●●Level 43 marksStart
A rectangle measures 1212 cm by 99 cm, each correct to the nearest centimetre.

Work out the upper bound of the perimeter.
●●●●●Level 42 marksStart
A rectangle measures 8.38.3 cm by 6.46.4 cm, each correct to 11 decimal place.

Work out the lower bound of the area of the rectangle.
●●●●●Level 42 marksStart
A car travels 120120 m, correct to the nearest 1010 m, in 15.615.6 seconds, correct to 1 decimal place.

(a) Work out the upper bound for the average speed of the car. Give your answer correct to 3 significant figures. (3 marks)

(b) Work out the lower bound for the average speed of the car. Give your answer correct to 3 significant figures. (1 mark)
●●●●●Level 44 marksStart
The radius of a circle is 6.46.4 cm, correct to 1 decimal place.

(a) Work out the upper bound for the circumference of the circle. [2]

(b) Work out the lower bound for the circumference. [1]

(c) Use your answers to write down the circumference to a suitable degree of accuracy. Explain your choice. [1]
●●●●●Level 44 marksStart
There are some wooden boards in a stack.

The height of the stack is 58.758.7 cm, correct to the nearest mm.

The thickness of each board is 1.81.8 cm, correct to 22 significant figures.

Calculate the upper bound for the number of boards in the stack.

You must show all your working.

(3 marks)
●●●●●Level 43 marksStart
M=ABM = \frac{A}{B}

A=7.26×105A = 7.26 \times 10^{5} correct to 33 significant figures.

B=4.8×102B = 4.8 \times 10^{2} correct to 22 significant figures.

Work out the upper bound for MM.

Give your answer as an ordinary number correct to the nearest integer.

You must show all your working.

(3 marks)
●●●●●Level 43 marksStart
A runner covers a distance of d=84d = 84 m, correct to the nearest metre, in a time of t=6.2t = 6.2 s, correct to 1 decimal place.

Work out the upper bound of the average speed dt\dfrac{d}{t}. Give your answer to 2 decimal places.
●●●●●Level 53 marksStart
k=abk = \dfrac{a}{b}, where a=5.4a = 5.4 and b=1.8b = 1.8, each correct to 1 decimal place.

By considering bounds, work out the value of kk to a suitable degree of accuracy. You must show all your working and give a reason for your answer.
●●●●●Level 54 marksStart
x=7.2x = 7.2 and y=4.5y = 4.5, each correct to 1 decimal place.

Work out the lower bound of x−yx - y.
●●●●●Level 53 marksStart
A cyclist covers a distance of d=150d = 150 m, correct to the nearest 1010 m, in a time of t=12.4t = 12.4 s, correct to 11 decimal place.

Work out the lower bound of the cyclist's average speed. Give your answer correct to 3 significant figures.
●●●●●Level 53 marksStart
v=xyv = \dfrac{x}{y}, where x=9.6x = 9.6 and y=3.2y = 3.2, each correct to 11 decimal place.

By considering bounds, work out the value of vv to a suitable degree of accuracy. You must show your working and give a reason for your answer.
●●●●●Level 54 marksStart
PQRPQR is a right-angled triangle.5.2 cm7.4 cmxPQRPQ=7.4PQ = 7.4 cm correct to the nearest mm.

QR=5.2QR = 5.2 cm correct to the nearest mm.

Calculate the upper bound for the size of the angle marked xx.

You must show all your working.

(3 marks)
●●●●●Level 53 marksStart