My Learning Outcome…I will learn…

How to round to whole numbers , decimal places and significant figures.

I will apply my learning by…

Rounding .

I will evaluate my learning by…

Explaining to your partner how to round to 1 significant figure?

L4Rounding to nearest 10 or 100.

L5Rounding to decimal places. L6Rounding to significant figures.

L7:

Be bale to understand standard form.

Learning Objective:

Application Tasks…

Key words: SquareTriangle

trapezium

Rounding – to the nearest 10

Yes

4 8 3 2No 5 or

more?

4 8 3 0

4 8 3 75 or

more?

4 8 4 0Yes

1 9 55 or

more?

2 0 0

L 4

Learn

Rounding – to the nearest 100

Yes

1 5 8 2 3 1 No

1 5 8 2 0 0

5 8 7 2 5 or

more?

5 9 0 0Yes

8 95 or

more?

1 0 0

Your

Tur

n

Copy & completethis table:

5 or more?

Number To nearest 10

To nearest 100

To nearest 1000

37 521274 503

7 630 918

9 875452

380003750037520275000274500274500

7631000763090076309201000099009880

0500450

L 4Apply

Rounding to 1 Decimal Place (1DP)

No

4 . 8 3 2 5No 5 or

more?

4 . 8

4 . 8 4 2 5 5 or

more?

4 . 8Yes

4 . 8 5 2 5 or

more?

4 . 9

Yes

4 . 8 7 Yes

5 or more?

4 . 9

5 . 2 6 7 1 4 5 or

more?

5 . 3Yes

1 . 9 6 7 5 or

more?

2 . 0

L 5 Learn

Rounding to Decimal Places: 2DP

Yes

4 . 8 3 2 5No 5 or

more?

4 . 8 3

4 . 8 4 6 5 or

more?

4 . 8 5Yes

4 . 8 5 9 5 1 5 or

more?

4 . 8 6

Yes

1 . 6 9 4 9No 5 or

more?

1 . 6 9

5 . 2 6 7 1 5 or

more?

5 . 2 7Yes

1 . 8 9 7 5 or

more?

1 . 9 0

L5Learn

Rounding to Decimal Places: 3DP

No

4 . 8 3 2 5Ye

s5 or

more?

4 . 8 3 3

4 . 8 4 6 2 5 or

more?

4 . 8 4 6

Yes

4 . 8 5 9 5 5 or

more?

4 . 8 6 0

Yes

1 . 6 9 4 2No 5 or

more?

1 . 6 9 4

5 . 2 6 2 7 5 or

more?

5 . 2 6 3

Yes

1 . 9 9 9 9 5 or

more?

2 . 0 0 0

L5Learn

Rounding to Decimal Places

Yes

5 . 2 6 2 7 5 or

more?

5 . 2 6 3

1 . 6 9 4 9No 5 or

more?

1 . 6 9Yes

4 . 8 5 2 5 or

more?

4 . 9

Your

Tur

n

Copy & completethis table:

Number To 1DP To 2DP To 3DP63.4721 87.6564149.987

53.540290.59999

63.5 63.47 63.47287.7 87.66 87.656

150.0 149.99 149.9883.5 3.54 3.5400.6 0.60 0.600

3DP2DP1DP

D

Apply

Significant Figures: Important Zeros in Numbers

5 2 0 0 05 . 2 0 00 . 0 5 00 2 . 5 0

a.

b.

c.

d.

Which zeros matter?

Are there any we could get rid of and still

have the same value?

When dealing with Significant Figures, you need to keep any zeros that tell us the value of a number

L6Learn

Rounding to 1 Significant Figure (1SF)

No

0 . 0 7 6 5Ye

s5 or

more?

0 . 0 8

0 . 0 0 1 2 5 or

more?

0 . 0 0 1

No

1 . 0 0 9 5 5 or

more?

1

Yes

2 4 1No 5 or

more?

2 0 0

5 8 7 5 or

more?

6 0 0 Yes

7 55 or

more?

8 0

L6Learn

Rounding to 2 Significant Figure (2SF)

No

1 4 7 2 Yes

5 or more?

1 5 0 0

1 . 4 2 7 9 5 or

more?

1 . 4Yes

0 . 0 5 3 5 5 or

more?

0 . 0 5 4

No

4 2 7 2 8 Ye

s5 or

more?

4 3 0 0 0

2 0 4 4 7 8 5 or

more?

2 0 0 0 0 0

Yes

0 . 0 6 9 6 5 or

more?

0 . 0 7 0

L6Learn

Rounding to 3 Significant Figure (3SF)

No

0 . 0 2 6 7 1No 5 or

more?

0 . 0 2 6 7

3 . 2 9 4 9 5 or

more?

3 . 2 9No

3 4 7 2 8 5 or

more?

3 4 7 0 0

Yes

1 3 7 9 8 Ye

s5 or

more?

1 3 8 0 0

9 7 4 9 7 8 5 or

more?

9 7 5 0 0 0

Yes

1 2 . 0 6 9 5 or

more?

1 2 . 1

L6Learn

Rounding to Significant FiguresYo

ur T

urn

Copy & completethis table:

Number To 1SF To 2SF To 3SF6.352834.026

0.005708150.932

0.00007835

3SF2SF1SF0 . 0 7 6 5Ye

s5 or

more?

0 . 0 8

4 2 7 2 8 Ye

s5 or

more?

4 3 0 0 0

Yes

1 2 . 0 6 9 5 or

more?

1 2 . 1

6.35 6.4 634.0 34 30

0.00571 0.0057 0.006151 150 200

0.0000784 0.000078 0.00008C

Apply

You need to understand about powers of 10.Try these to test your previous knowledge.

102

103

10-2

106 10-3 Remember this?

100 101

10-1

(Use the worksheet “powers of ten” for further explanation)

105

104

Learn

Standard Form is used a lot in maths andscience as a convenient way of writing very

large, or very small numbers for example:

The distance from the earth to the sun is149 000 000 km

A hydrogen atom has a diameter of about

0.000 000 2 mm

huge!

microscopic!

Learn

Let’s deal with large numbers first.Look at how these numbers have been broken down:

500 = 5 × 100

5000 = 5 × 1 000

50 000 = 5 × 10 000you know how to writethese as powers of 10

= 5 × 102

= 5 × 103

= 5 × 104

Learn

What about these?

550

5 500

55 000

= 5.5 × 100 = 5.5 × 102

= 5.5 × 1 000

= 5.5 × 10 000

= 5.5 × 103

= 5.5 × 104

Learn

Put these numbers into standard form:

6 000

9 0004 00 000

80 000

400 4504 000

550003500

750 000

= 6 × 103

= 4 × 102

= 8 × 104

= 9 × 103

= 4 × 105

= 4 × 103

= 4.5 × 102

= 5.5 × 104

= 3.5 × 103

= 7.5 × 105

Learn

Standard form is:

a number between 1

and 10 × a power of ten

but not including 10 positive or negative

Learn

Now try writing these numbers in standard form:

5 000 000

5 500 000

5 250 000

5 100 000

5 156 342

= 5 × 106

= 5.5 × 106

= 5.25 × 106

= 5.1 × 106

= 5.156342 × 106

Apply

Reverse! Change each of these numbers to an ordinary number

6 × 102

2 × 103

5 × 107

9 × 108

3.7 × 109

2.8 × 101

9.9 × 1010

7.1 × 104

3.97 × 102

8.172 × 102

Learn

The next stage is to write very small numbers, i.e. numbers less than 1

Check that you understand about negative powers of 10

0.1 = 1 = 10-1

10

0.001 =

0.00001 =0.01 =

0.0001 =

Learn

Write in standard form:

0.007

0.04

0.000 000 005

0.0234

0.000 002 3

0.006 7

0.000 000 002 34

0.006 7

0.3

0.000 045

Apply

*Change to small numbers3.5 × 10-1

4.5 × 10-4

7.2 × 10-5

6.1 × 10-3

1.17 × 10-10

Apply

Change each of these to a large or small number:

5.5 × 10-6

6.5 × 10-8

3.2 × 105

2.9 × 102

3.167 × 10-11

1.115 × 104

1.412 × 10-3

7.2 × 101

9.01 × 10-2

1.17 × 106

Apply

*Evaluate

*How do you round to the nearest Significant figure?