Year 8

# Upper and Lower Bound

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## Lesson details

### Key learning points

- In this lesson, we will learn what upper and lower bound mean and how this links with range.

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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.

A teacher asked two students to round the number 5,469,704. Their answers are below. Which student(s) rounded the number correctly? Explain your answer.

Neither students are correct.

Student A said that the number rounds to 5,000, 000

Student B said the number rounds to 5,500,000

Q2.

I think about a number and rounds it to the nearest hundred. My answer is 5300. What is the greatest possible number I could have thought of?

5250

5299

5399

Q3.

Halima is planning a concert to raise money for charity. Entry to the concert is £5.00. The number of people attending the concert is 700 to the nearest hundred. What is the lowest possible amount of money she raised for charity?

£3,542

£32.50

3,745

Q4.

The population of Northern Ireland is 1.9 million, to the nearest hundred thousand. What is the lowest possible number of people that live in N.Ireland?

1,849,999

1,899,000

1,949,999

Q5.

The population of Northern Ireland is 1.9 million, to the nearest hundred thousand. What is the greatest possible number of people that live in N.Ireland?

1,850,000

1,899,999

1,949,000

Q6.

The population of Birmingham is 1.1 million rounded to nearest hundred thousand. What is the range of values for the population of Birmingham?

1,050,000 ≤ x 1,100,000

1,050,000 ≤ x <1,099,000

### 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