Accuracy.pptx

EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Accuracy

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Lesson 1 of 9

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up

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Lesson 1 of 9

Answer each one, then check.

1

Round 3.47 to 1 decimal place.

2

Round 4650 to the nearest 100.

3

What does < mean?

4

What does ≤ mean?

5

Round 0.0364 to 2 significant figures.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Warm-up - Answers

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Lesson 1 of 9

1

Round 3.47 to 1 decimal place.

3.5

2

Round 4650 to the nearest 100.

4700

3

What does < mean?

Less than

4

What does ≤ mean?

Less than or equal to

5

Round 0.0364 to 2 significant figures.

0.036

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Learning Objectives

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Lesson 1 of 9

1

Find the upper and lower bounds of a rounded number.

2

Write an error interval using inequalities.

3

Find bounds for sums, differences, products and quotients (Higher).

4

Choose a sensible degree of accuracy for an answer.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

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Lesson 1 of 9

BOUNDS

A rounded value could have started anywhere in a range: half a unit either side of it.

If a number is rounded to the nearest 10, the range is 5 either side. Nearest 1: 0.5 either side. Nearest 0.1: 0.05 either side.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Bounds on a Number Line

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Lesson 1 of 9

Closed circle: included. Open circle: not included.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Finding Bounds

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Lesson 1 of 9

A length is 8.3 cm, rounded to 1 decimal place. Write down the lower bound and the upper bound.

1

Rounding unit

0.1, so half a unit is 0.05

2

Lower bound

8.3 − 0.05 = 8.25

3

Upper bound

8.3 + 0.05 = 8.35

ANSWER

Lower bound 8.25 cm, upper bound 8.35 cm.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Writing an Error Interval

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Lesson 1 of 9

n = 350 to the nearest 10. Write the error interval for n.

1

Half a unit

5

2

Lower bound is included

345 ≤ n

3

Upper bound is not included

n < 355

ANSWER

345 ≤ n < 355

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Rounding and Bounds

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Lesson 1 of 9

Half a unit each way.

Rounded to

Value

Error interval

Nearest 10

60

55 ≤ x < 65

Nearest whole number

7

6.5 ≤ x < 7.5

1 decimal place

2.4

2.35 ≤ x < 2.45

2 significant figures

0.83

0.825 ≤ x < 0.835

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Bounds in Calculations (Higher)

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Lesson 1 of 9

BIGGEST POSSIBLE ANSWER

• Add: use both upper bounds.

• Subtract: upper bound minus lower bound.

• Multiply: upper times upper.

• Divide: upper bound divided by lower bound.

SMALLEST POSSIBLE ANSWER

• Add: use both lower bounds.

• Subtract: lower bound minus upper bound.

• Multiply: lower times lower.

• Divide: lower bound divided by upper bound.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Bounds of a Rectangle's Area (Higher)

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Lesson 1 of 9

A rectangle has length 12 cm and width 5 cm, both to the nearest centimetre. Find the greatest possible area.

1

Upper bound of length

12.5

2

Upper bound of width

5.5

3

Multiply

12.5 × 5.5 = 68.75

ANSWER

68.75 cm²

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Sensible Accuracy

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Lesson 1 of 9

Do not give an answer more accurately than the data allows.

Round at the end

Keep full calculator values until the last step.

Match the data

If measurements are to 2 significant figures, do not quote 6 in the answer.

Bounds agree

If the upper and lower bounds of an answer round to the same value, that value is the answer to that accuracy.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Key Terms

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Lesson 1 of 9

Lower bound

The smallest value that rounds to the given number.

Upper bound

The value at the top of the range; not itself included.

Error interval

The range of possible values written with inequalities.

Degree of accuracy

How precisely a value is given, e.g. 1 d.p. or 2 s.f.

Truncate

Cut off digits without rounding.

Significant figures

Digits that carry meaning, counting from the first non-zero digit.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

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Lesson 1 of 9

YOUR TASK

Bounds Race

10 minutes

Find the error interval for each value. (a) 6.8 to 1 d.p. (b) 1200 to the nearest 100 (c) 0.05 to 1 significant figure (d) 25 to 2 significant figures.

1

Find the rounding unit.

2

Halve it and add and subtract.

WHAT A GOOD ANSWER SHOWS

(a) 6.75 ≤ x < 6.85 (b) 1150 ≤ x < 1250 (c) 0.045 ≤ x < 0.055 (d) 24.5 ≤ x < 25.5

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Can I...?

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Lesson 1 of 9

Find the rounding unit.

Write a lower bound.

Write an upper bound.

Write an error interval.

Use the right inequality signs.

Find bounds for an addition or subtraction.

Find bounds for a product or quotient.

Choose a sensible accuracy.

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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER

Summary & Exam Focus

Half a unit each side of the rounded value.

Lower bound included, upper bound not.

Bounds calculations: choose the extreme values that make the answer largest or smallest.

Do not round until the final answer.

EXAM FOCUS

x = 7.4 to 1 decimal place. Write down the error interval for x. (2 marks)

Lower bound uses ≤; upper bound uses <.

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