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### Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

### Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

### Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

GCSE Maths Starter 18

4. Write these numbers in order of size, smallest first:

1.8, 3.71, 0.5, 12.4

5.

- Write down the reciprocal of ¼
- A small pot costs 20 pence. A large pot costs 150% more, how much does the large pot cost?
- Copy the pattern into your book, add one more square so the pattern has one line of symmetry

To round numbers to a given degree of accuracy (Grade E )

To use your calculator to solve numerical problems (Grade E/D)

EXTN:

To calculate an estimate for a given sum (Grade C)

Significant Figures (Rounding)

Numbers can be rounded to 1,2, 3 or more significant figures. We count the number of figures from the firstnon-zero digit.

First non-zero digit.

Rounding to 1 s.f

5 or bigger ?

5 or bigger ?

5 or bigger ?

4

6

0.04

4 . 3 3 2 5

0. 0 4 2 5

5. 7 4 2 5

No

No

Yes

First non-zero digit.

5 or bigger ?

5 or bigger ?

0.08

0.002

Significant Figures (Rounding)

Rounding to 1 s.f

0. 0 0 1 5

0 . 0 7 6

Yes

Yes

5 or bigger ?

5 or bigger ?

1.5

0.054

Significant Figures (Rounding)

Rounding to 2 s.f

1 . 4 7 2 9

0. 0 5 3 5

Yes

Yes

5 or bigger ?

5 or bigger ?

0.0205

2.08

Significant Figures (Rounding)

Rounding to 3 s.f

2 . 0 7 5 9

0. 0 2 0 4 6 3

Yes

Yes

Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

The following number could be the population of a country at a particular instant in time.Write this number to 1, 2, 3, 4, 5, 6 and 7 significant figures.

56 345 678

56 000 000

56 300 000

60 000 000

56 345 700

56 350 000

56 346 000

56 345 680

Estimation

“is approximately equal to”

Martin uses his calculator to work out 39 × 72.

The display shows an answer of 1053.

How do you know this answer must be wrong?

39 × 72

40 × 70 =

2800

Also, if we multiply together the last digits of 39 and 72 we have

9 × 2 = 18.

9 × 2 = 18.

The product of 39 and 72 must therefore end in an 8.

Estimation

How could we estimate the answer to 3.5 × 17.5?

3.5 × 17.5 can be approximated to:

4 × 20 =

80

3 × 18 =

54

4 × 17 =

68

or between 3 × 17 =

51

and 4 × 18 =

72

Estimation

How could we estimate the answer to 4948 ÷ 58?

4948 ÷ 58 can be approximated to:

5000 ÷ 60 =

?

(60 does not divide into 5000)

5000 ÷ 50 =

100

4950 ÷ 50 =

99

or 4800 ÷ 60 =

80

Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

Estimate the following. (Clearly show your rounded values)

1500

20,000

8,000,000

1) 29 × 512) 431 × 48 3) 2184 × 3962

4) 17.41 × 8.73 5) 4.372 × 1.821 6) 5.32 × 0.236

7) 0.731 × 0.489 8)0.0813 × 0.279) 1.043 × 4.21

10) 2.73 × 4.1 × 6.211) 2.43 × 0.045 × 3 12) 0.23 × 2.74 × 3.05 × 0.97

180

8

1

0.35

0.024

4

0.3

72

1.8

Solving complex calculations mentally

3.2 + 6.8

What is

?

7.4 – 2.4

3.2 + 6.8

10

=

=

7.4 – 2.4

5

2

We could also write this calculation as: (3.2 + 6.8) ÷ (7.4 – 2.4).

How could we work this out using a calculator?

Using bracket keys on the calculator

3.7 + 2.1

What is

?

3.7 – 2.1

3.7 + 2.1

6

=

3.7 – 2.1

2

We start by estimating the answer:

3

Using brackets we key in:

(3.7 + 2.1) ÷ (3.7 – 2.1) =

3.625

Four people used their calculators to work out .

15 – 7

Tracy gets the answer 4.

Fiona gets the answer 4.875.

Some for you to try..

Andrew gets the answer –4.4.

Sam gets the answer 12.75.

Who is correct?

What did the others do wrong?

Some for you to try..

Lesson 18 Estimation and using a calculatorMathswatch clip (14/101/63).

Exam questions

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