# Solving Problems with Rounding

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## Lesson details

### Key learning points

- In this lesson, we will learn how to solve problems working with lower and upper bounds to find maximum and minimum values.

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This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

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### 6 Questions

Q1.

Write down an inequality expressing the lower and upper bound for 23.071kg to three decimal places

23.0705 ≤ k < 23.0714

23.0705 ≤ k ≤ 23.0715

23.0710 ≤ k < 23.0715

Q2.

Write down an inequality expressing the lower and upper bound for 0.3m given to 1 significant figure

0.25 < m ≤ 0.35

0.25 ≤ m ≤ 0.35

0.25 ≤ m < 0.349999

Q3.

Write down an inequality expressing the lower and upper bound for 0.023 given to 2 significant figure

0.0224 ≤ x < 0.0235

0.0225 ≤ x ≤ 0.02349

LB = 0.0225 , UB = 0.0235

Q4.

The length of a football field is 500m to the nearest 10m. Jacob says the lower bound is 450m and the upper bound is 550m. Is he correct? Give a reason for your answer.

Yes, he is correct

Q5.

The mass of a loaf of bread is given as 1.7kg to the nearest 0.1kg. Write an inequality expressing the upper and lower bound of the mass.

1.645kg ≤ m ≤ 1.745kg

1.649kg ≤ m < 1.749kg

1.65kg ≤ m ≤ 1.75kg

Q6.

A piece of string is measured at 1.57m to two decimal places. Write an inequality expressing the lower and upper bound within which l, the actual length of string lies.

1.564999 ≤ l ≤1.574999

1.565 ≤ l < 1.570

1.565 ≤ l ≤1.575

### 6 Questions

Q1.

A classroom is measured 5.4 x 3.4 metres, measured to 1 d.p. Calculate the lower bound of the area of the room.

17.889 𝑐𝑚^2

18.36 𝑐𝑚^2

18.8025 𝑐𝑚^2

Q2.

James ran a distance of 400m in a time of 25.2 seconds. The distance of 400m was measured to the nearest 10 metres. The time of 25.2 was measured to the nearest tenth of a second. Work out the upper bound James' average speed.

15.7 m/s

16.04 m/s

16.07 m/s

Q3.

James ran a distance of 400m in a time of 25.2 seconds. The distance of 400m was measured to the nearest 10 metres. The time of 25.2 was measured to the nearest tenth of a second. Work out the lower bound James' average speed.

15.67 m/s

15.69 m/s

15.71 m/s

Q4.

Carl measured the length and width of a rectangle. He measured the length to be 19cm correct to the nearest centimetre. He measured the width to be 20cm correct to the nearest 10cm. Calculate the lower bound for the area of this rectangle.

292.5 cm^2

370 cm^2

380 cm^2

Q5.

6 heights are listed, given to one decimal place: 4.6cm, 6.3cm, 9.8cm, 3.2cm, 5.7cm, 3.6cm. Work out the greatest possible mean.

5.48cm

5.53cm

5.98cm

Q6.

A circle has an area of 130cm^2 to the nearest 10cm^2. Work out the upper bound of the radius. Give your answer to 3 d.p.

39.789

6.308

6.433