Rounding, Estimation & Bounds

Steve travelled from Ashton to Barnfield.

   He travelled miles, correct to the nearest  miles.
   The journey took him  minutes, correct to the nearest  minutes.

   Calculate the lower bound for the average speed of the journey.
   Give your answer in miles per hour, correct to  significant figures.
   You must show all your working.

Jarek uses the formula

to work out the area of a triangle.

For this triangle,

Calculate the lower bound for the area of the triangle.

is 8.3 cm correct to the nearest mm
is 6.1 cm correct to the nearest mm

Calculate the upper bound for .
You must show your working.

A train travelled along a track in 110 minutes, correct to the nearest 5 minutes.

Jake finds out that the track is 270 km long.
He assumes that the track has been measured correct to the nearest 10 km.

Could the average speed of the train have been greater than 160 km/h?
You must show how you get your answer.

Jake's assumption was wrong.
The track was measured correct to the nearest 5 km.

Explain how this could affect your decision in part (a).

The petrol consumption of a car, in litres per 100 kilometres, is given by the formula

         

Nathan's car travelled 148 kilometres, correct to 3 significant figures.
The car used 11.8 litres of petrol, correct to 3 significant figures.

Nathan says,

   "My car used less than 8 litres of petrol per 100 kilometres."

Could Nathan be wrong?
You must show how you get your answer.

A cone has a volume of 98 cm³.
The radius of the cone is 5.13 cm.

Work out an estimate for the height of the cone.

John uses a calculator to work out the height of the cone to 2 decimal places.

Work out an estimate for 

Margaret has some goats.
The goats produce an average total of 21.7 litres of milk per day for 280 days.
Margaret sells the milk in  litre bottles.

Work out an estimate for the total number of bottles that Margaret will be able to fill with the milk.
You must show clearly how you got your estimate.

In a competition, a prize is won every 2014 seconds.

Work out an estimate for the number of prizes won in 24 hours.
You must show your working.

The mass of Jupiter is 1.899 x 10²⁷ kg.
The mass of Saturn is 0.3 times the mass of Jupiter.

Give evidence to show whether your answer to (a) is an underestimate or an overestimate.

Calculate the upper bound for the value of .
Give your answer correct to  significant figures.
You must show all your working.

The lower bound for the value of  is  correct to  significant figures.

By considering bounds, write down the value of to a suitable degree of accuracy.
You must give a reason for your answer.

Edith’s van can safely carry a maximum load of 920 kilograms.

She wants to use her van to carry

30 sacks of potatoes, each of mass 25 kilograms to the nearest kilogram

and

20 sacks of carrots, each of mass 7.5 kilograms to 1 decimal place.

Can she definitely use her van safely in one journey?

You must show your working.

The length of a roll of ribbon is 30 metres, correct to the nearest half-metre.

A piece of length 5.8 metres, correct to the nearest 10 centimetres, is cut from the roll.

Work out the maximum possible length of ribbon left on the roll.

...................metres

Claudine cycled a distance of 53 km in 2.7 hours.
The distance is measured correct to the nearest km.
The time is given correct to 1 decimal place.

Calculate the lower and upper bounds of her average speed.

Give your answers correct to 2 decimal places.

Lower bound = ................................ km/h     
Upper bound = ..................................... km/h

Sunil makes 7.5 litres of soup, correct to the nearest 0.5 litre.
He serves the soup in 300 ml portions, correct to the nearest 10 ml.
24 people order this soup.

Does Sunil definitely have enough soup to serve the 24 people?
Show how you decide.

Work out the upper bound for the value of .
You must show your working.

Work out the upper bound for the value of .
Show your working clearly.

Work out an upper bound for .

There are litres of oil in Mr Aston's oil tank.
He uses litres of oil each day.

Estimate the number of days it will take him to use all the oil in the tank.

Work out an estimate for 

Work out an estimate for the value of  .

correct to  significant figures.

Find the value of correct to  significant figures.

Show that

Sally used her calculator to work out the value of a number .
The answer on her calculator display began

Complete the error interval for .

............................ ....................

= 14 correct to 2 significant figures
= 7.8 correct to 2 significant figures
= 3.4 correct to 2 significant figures

Work out the lower bound for the value of .
Show your working clearly.

Nav has worked out  on his calculator.

His answer is 

Without using a calculator and using suitable approximations, check that his answer is sensible.
Show your working clearly.

Work out the lower bound for the value of .
Show your working clearly.
Give your answer correct to  significant figures.

Work out the upper bound for the value of .
Show your working clearly.
Give your answer correct to  significant figures.

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To the nearest pound, Jon has £9

To the nearest 50p, Ellie has £6.50

Work out the maximum possible total amount of money.

£........................................ 

The length of a pipe is 6 metres to the nearest metre.

Complete the error interval for the length of the pipe.

...........................m ⩽ length < ...........................m

he length of a different pipe is 4 metres to the nearest metre.

Olly says,

“The total length of the two pipes is 11 metres to the nearest metre.”

Give an example to show that he could be correct.

The dimensions of a rectangular floor are to the nearest 0.1 metres.

A force of 345 Newtons is applied to the floor.
The force is to the nearest 5 Newtons.

Work out the upper bound of the pressure.
Give your answer to 4 significant figures.
You must show your working.

........................N/m² [5]

A £1 coin weighs 8.75 g, correct to the nearest 0.01 g.
Mitul weighs the contents of a large bag of £1 coins.
The coins weigh 2.63 kg, correct to the nearest 10 g.

Mitul says

   I am sure that the bag contains exactly £300 because, using bounds,
   2625 ÷ 8.755 = 299.8 to 1 decimal place.

Show that Mitul may not be correct.

[3]