A cuboid has length 2 cm and width 4 cm, each correct to the nearest integer. Its volume is \(123.8\text{ cm}^3\), correct to 1 decimal place.

Find the lower bound of its height. [3]

Beth runs 28 km, correct to the nearest kilometre. Her average speed is 10 km/h, correct to the nearest 1 km/h. Find the upper bound of her running time in hours. [3]

A metal cuboid has volume \(22\text{ cm}^3\), correct to the nearest \(\text{cm}^3\), and mass \(140\text{ g}\), correct to the nearest \(10\text{ g}\). Find the lower bound of density, using density = mass ÷ volume. [3]

A rectangle is \(4.2\text{ cm}\) by \(6.8\text{ cm}\), each correct to the nearest millimetre. Find the lower bound of its area. [2]

\(D=\sqrt{\frac{1.95\times9.92^2}{8.07}}\). Round each number to 1 significant figure and estimate D. [3]

A metal piece has volume \(1240\text{ cm}^3\), correct to the nearest \(20\text{ cm}^3\), and mass 7800 g, correct to the nearest 100 g. Find the lower density bound (density = mass ÷ volume). [3]

\(I=V/R\). V is 50 correct to the nearest 10, and R is 13 correct to the nearest integer. Find the upper bound of I. [3]

A rectangle has length 16 cm and width 14 cm, each correct to the nearest centimetre. Find the lower bound of its perimeter. [2]

A metal cube has mass 14.2 g, correct to 1 decimal place.

(a) Find the lower bound of its mass. [1]

(b) Its edge length is 1.3 cm, correct to 1 decimal place. Find the upper bound of its density (mass ÷ volume). [3]

Nina walks at 5 km/h, correct to the nearest km/h, for exactly 2 hours. Find the lower bound of her distance. [2]

A solid metal prism has mass 4810 g to the nearest 10 g and density 7.7 g/cm³ to 1 decimal place. Find the lower bound of its volume. Density = mass ÷ volume. [3]

A wire is 68 cm long to the nearest centimetre. Jenna cuts off pieces 4.7 cm and 10.0 cm long, each to the nearest millimetre. Find the lower and upper bounds of the remaining length. [3]

Write 0.04628 to 2 significant figures. [1]

A rectangle has area 150 m² to the nearest square metre and length 22 m to the nearest metre. Find the upper bound of its width. [3]

A journey is \(14\text{ km}\), correct to the nearest kilometre, and takes \(12\text{ minutes}\), correct to the nearest minute.

Calculate the lower bound for the average speed, in km/min. [3]

By rounding each number to 1 significant figure, estimate \(\frac{6.7\times2.1}{18-5.9}\). Show all your working. [2]

Two stations are 220 km apart, correct to the nearest kilometre. The train speed is 125 km/h, correct to the nearest 5 km/h.

Calculate the upper bound for the journey time, in hours and minutes. [4]

Write 24.07839

(a) correct to 2 decimal places. [1]

(b) correct to the nearest 10. [1]

\(P=2w+2h\), where \(w=11,h=9.5\) are each correct to 2 significant figures.

Find the lower and upper bounds for \(P\). [3]

A rectangle has area \(55.2\text{ cm}^2\) to 1 decimal place and length 9 cm to the nearest cm. Calculate the upper bound of its width. [3]

Ribbon length is 23 cm to the nearest cm. A piece of 87 mm to the nearest mm is cut off. Find lower and upper bounds of remaining length in centimetres. [3]

Violet and Wilfred run 200 m in 36 s and 39 s, each to the nearest second. Find the upper bound for the difference. [2]

Estimate \(\frac{2.8\times82.6}{27.8-13.9}\) by rounding every number to 1 significant figure. [2]

(a) A rice bag has mass 25 kg to the nearest kg. Find the lower bound of the total mass of 10 such bags. [1]

(b) A wire has length 200 m to the nearest metre. It is cut into n pieces, each 3 m to the nearest 20 cm. Find the largest possible n. [3]

A regular hexagon has sides of 80 mm to the nearest millimetre. Find the lower bound of its perimeter. [2]

A journey is 600 km to the nearest 10 km and takes 8 hours 40 minutes to the nearest 10 minutes. Find the lower bound for its average speed in km/h. [3]

A car at constant speed travels 146.2 m, correct to 1 decimal place, in 7 seconds, correct to the nearest second. Calculate the upper bound of its speed. [3]

Given \(P=2(w+h)\), w = 12 and h = 4, both to the nearest whole number, find the upper bound for P. [2]

Ella’s height is 175 cm to the nearest 5 cm. Find its upper bound. [1]

Estimate \(T=\frac{49.2-9.595}{4.085\times2.35}\) by rounding each number to1 significant figure. Show working. [2]

An isosceles triangle has side measurements8.2 cm and9.4 cm, each correct to the nearest millimetre. Find the largest possible perimeter. [3]

A line has measured length18.3 cm, correct to the nearest millimetre. State the range for its true length l in cm. [2]

(a) Round0.046875 to2 significant figures. [1]

(b) Write2760000 in standard form. [1]

An equilateral triangle has sides of length 15 cm, correct to the nearest centimetre. Calculate the upper bound of its perimeter. [1]

(a) Write 0.047883 correct to 2 significant figures. [1]

(b) Write 0.00527 in standard form. [1]

Write 1.8972 correct to 2 decimal places. [1]

\(A=\frac{bh}2\), A=10 and h=4, both correct to the nearest whole number. Find the upper bound of b. [3]

Square side 15.1 cm is correct to 1 decimal place. Find the upper bound of its area. [2]

Anna walks 31 km at 5 km/h. Both values are correct to the nearest whole number. Find the upper bound of the time. [2]

(a) A square’s side is 12 cm, to the nearest centimetre. Find the upper bound for its perimeter. [2]

(b) Jo records a rope’s length to the nearest ten centimetres. Its upper bound is 12.35 m. State her recorded measurement. [1]

(a) Round 209 802 to the nearest thousand. [1]

(b) Round 4123 to 3 significant figures. [1]

Saafia has 6000 ml of oil, to the nearest 100 ml. Bottles hold exactly 50 ml. Calculate the upper bound for the number of bottles she can fill. [2]

An equilateral triangle has side 12 cm, to the nearest centimetre. Find the lower and upper bounds of its perimeter. [2]

A square has area 42.5 cm², to the nearest 0.5 cm². Find the lower bound of its side length. [2]

Write each number correct to 2 significant figures.

(a) 0.076499. [1]

(b) 10 100. [1]

Without a calculator, round each number to 1 significant figure to estimate \(\frac{10.3\times19.5}{88.9-43.2}\). Show all working. [2]

A rectangle has length 9.3 cm and width 7.7 cm, both correct to 1 decimal place. Write the lower and upper bounds for its area. [3]

Write 23.4571 correct to

(a) 4 significant figures. [1]

(b) the nearest 10. [1]

Write 0.07164 correct to 2 significant figures. [1]

A rectangle has length 62 mm and width 47 mm, both correct to the nearest millimetre. Its area is A mm². Complete \(\ldots\le A<\ldots\). [3]

In 2016 a company sold 9600 cars, correct to the nearest hundred.

(a(i)) Write the lower bound for the number sold. [1]

(a(ii)) Average profit per car was \$2430, correct to the nearest \$10. Calculate the exact lower bound for total profit. [2]

(a(iii)) Write this profit to 4 significant figures. [1]

(a(iv)) Write the answer to (iii) in standard form. [1]

(b) April sales of 546 cars were 5% higher than March sales. Find March sales. [3]

(c) A new car cost \$3000 in 2013. Its price grows exponentially by 3% per year. Find the price 4 years later. [2]

Triangle sides are 5.2,6.3,9.4 cm, each to the nearest millimetre. Find the lower bound of its perimeter. [2]

(a) Calculate \(\frac{5^{0.4}-\sqrt3}{0.13-0.015}\) and write all digits in the calculator display. [1]

(b) Give the answer to 2 significant figures. [1]

Three identical cuboids form a tower. One cuboid’s height is 6.5 cm, correct to the nearest millimetre.

Find the upper bound for the tower’s height. [2]

A metal pole is 500 cm long, correct to the nearest centimetre. It is cut into rods of length 5.8 cm, correct to the nearest millimetre.

Calculate the largest possible number of rods. [3]

Calculate \((2.1-0.078)^{17}\), giving your answer correct to 4 significant figures. [2]

Write 3.5897 correct to 4 significant figures. [1]

Write 71496 correct to 2 significant figures. [1]

Each side of an equilateral triangle is 9.4 cm, correct to the nearest millimetre.

Work out the upper bound of its perimeter. [2]

A triangle has base 9 cm, correct to the nearest centimetre, and area 40 cm², correct to the nearest 5 cm².

Calculate the upper bound of its perpendicular height. [3]

In an experiment:

(a) \(V=IR\). I and R are measured correct to 1 decimal place. When \(I=4.0\) and \(R=2.7\), find the lower bound of V. [2]

(b) \(S=\frac DT\). D and T are measured correct to 2 significant figures. When \(D=7.6\) and \(T=0.23\), find the upper bound of S. [2]

(a) Round 14835 to the nearest thousand. [1]

(b) Write the answer to (a) in standard form. [1]

A square has side length 8 cm, correct to the nearest centimetre.

Calculate the upper bound for its area. [2]

A car has length 4.2 m, correct to 1 decimal place.

Write the upper and lower bounds of its length. [2]

Round 0.0401907 to:

(a) 3 significant figures; [1]

(b) 3 decimal places. [1]

Rice packs have masses 75 g and 120 g, each to the nearest gram. Find the lower bound for the difference in mass. [2]

Ahmed was 114 cm tall a year ago and is 120 cm tall today. Both are to the nearest cm. Find the upper bound of the increase. [2]

An equilateral triangle has each side 6.2 cm to the nearest millimetre. Complete \(\ldots\le P<\ldots\) for its perimeter P in cm. [2]

Round each number to 1 significant figure to estimate \(\frac{\sqrt{3.9}\times29.3}{8.9-2.7}\). Show working. [2]

A rectangle’s length is 5.8 cm and width 2.4 cm, both to 1 decimal place. Find the lower and upper bounds of its perimeter. [3]

Round 168.9 to 2 significant figures. [1]

Cuboid volume 878 cm³ is correct to the nearest cm³; base length 7 cm and width 6 cm are correct to the nearest cm. Find the lower bound of its height. [3]

1 cm³ of copper has mass 8.5 g, correct to 1 decimal place. Complete the bounds for mass T g of 12 cm³. [2]

\(p=4.8\times1.98276/16.83\).

(a) Write each number correct to 1 significant figure. [1]

(b) Use these rounded numbers to estimate p. [1]

A rectangle has length 127.3 cm and width 86.5 cm, each correct to 1 decimal place. Find upper and lower perimeter bounds. [3]

Round 15.0782 to

(a) one decimal place; [1]

(b) the nearest 10. [1]

A pitch length l metres is 96 m to the nearest metre. Complete \(\cdots\le l<\cdots\). [2]

Joe measures a square’s side to 1 decimal place. The upper bound of its area is 37.8225 cm². Find his measurement. [2]

Each side of an equilateral triangle is 16.1 cm, correct to the nearest millimetre.

Find the lower and upper bounds of its perimeter. [2]

A car’s length p cm is recorded as 440 cm to the nearest 10 cm. Complete the bounds statement. [2]

A circle’s radius is 8.5 cm to the nearest 0.1 cm. Its area has lower bound \(p\pi\) cm² and upper bound \(q\pi\) cm². Find p and q. [3]

A rectangle’s sides are 6.3 cm and 4.8 cm, each rounded to 1 decimal place. Find the upper bound of its area. [2]

There were 82 000 spectators, correct to the nearest thousand. Each paid R2600. Find the lower bound of the total paid and write it in standard form. [3]

A carton contains 250 ml of juice, correct to the nearest millilitre. Complete \(\ldots\le j<\ldots\) for the actual amount j ml. [2]

A bottle holds 25 litres, correct to the nearest litre. A glass holds 0.3 litres, correct to the nearest 0.1 litre. Find the lower bound for the number of full glasses that can be filled. [3]

(a) Round 7682 to one significant figure. [1]

(b) Round 0.07682 to one significant figure. [1]

Ashraf takes 1500 steps of length 90 cm, correct to the nearest 10 cm. Find the lower and upper bounds of his distance d metres. [3]

A rectangular sheet is 197 mm by 210 mm, each to the nearest millimetre. Find the upper bound of its perimeter. [2]

A rectangular photograph measures 23.3 cm by 19.7 cm, each to one decimal place.

(a) Find the lower bound of its perimeter. [2]

(b) Find the lower bound of its area. [1]

Making one chair costs \$28 to the nearest dollar. Find the lower and upper bounds of the cost of 450 chairs. [2]

A city’s population is 128000, to the nearest thousand.

(a) Write 128000 in standard form. [1]

(b) State the upper bound. [1]

\(72=2^3\cdot3^2\).

(a)(i) Write 126 as a product of prime factors. [2]

(a)(ii) Find the HCF of 72 and 126. [1]

(a)(iii) Find their LCM. [2]

(b) A pizza circumference is 105 cm and diameter is 34 cm, both to the nearest cm. Find the lower bound of the estimate of π, to 3 decimal places. [4]

(c) A cylindrical can has volume 550 cm³ to the nearest 10 cm³, and height 12 cm to the nearest cm. Find the upper bound of its radius, to 3 decimal places. [5]

A fence uses 32 identical pieces of wood, each 2 m long to the nearest centimetre. Find the lower bound of their total length, giving the full calculator display. [3]

An equilateral triangle has side 74 mm, to the nearest millimetre. Find its smallest possible perimeter. [2]

Round each number to 1 significant figure and estimate \(2.65(4.1758)+7.917\). Show working. [2]

A regular hexagon has side 6.8 cm, correct to one decimal place. Find its smallest possible perimeter. [2]

One wheel turn moves a car 120 cm, correct to the nearest centimetre. Find lower and upper bounds for 20 turns. [2]

A square side is 6.3 cm, correct to the nearest millimetre. Its perimeter lower bound is u cm and upper bound v cm.

(a) Find u. [1]

(b) Find v−u. [1]