Scientific notation

Standard Form (Scientific Notation) Lets start with very large numbers

Earth

Mercury

77,000,000km

Earth How far is it between Earth and the other planets in our solar system?

Saturn

1,517,000,000km

Earth

Uranus

1,747,200,000km

Standard Form (Scientific Notation) Lets start with very large numbers

Pteranodon

T­rex

How long ago were the dinosaurs around?

230,000,000yrs

Triceratops

Standard Form (Scientific Notation) Challenge

How many seconds are in a year?

1 year = 365days 1 year = 365 x 24 = 8760hrs 1 year = 8760 x 60 = 525600mins

1 year = 525600 x 60 = 31536000secs

Standard Form (Scientific Notation)

Standard Form (Scientific Notation) Writing numbers in a more compact way

10 = 101

100 = 10 x 10 = 102 1000 = 10 x 10 x 10 = 103

10000 = 10 x 10 x 10 x 10 = 104 100000 = 10 x 10 x 10 x 10 x 10 = 105 We can use this technique to help us with all large numbers

Standard Form (Scientific Notation) Writing numbers in a more compact way

300 = 3 x 100 = 3 x 102 4000 = 4 x 1000 = 4 x 103 70000 = 7 x 10000 = 7 x 104

900000 = 9 x 100000 = 9 x 105

2000000 = 2 x 1000000 = 2 x 106 We can use this technique to help us with all large numbers

Standard Form (Scientific Notation) Writing numbers in a more compact way

3200 = 32 x 100 = 32 x 102 This looks ok however in standard form this number must be between 1 and 10

3

3200 = 3.2 x 1000 = 3.2 x 10

We can use this technique to help us with all large numbers

Standard Form (Scientific Notation) A quick way to change to standard form(scientific notation)

345000 Move the decimal point till it comes after the first digit

3 45

Count how many places you moved the point Use this number as the power of 10

5

345000 = 3.45 x 10

TJ p188

Standard Form (Scientific Notation) Can we now write these in scientific notation?

Earth

Mercury

77,000,000km = 7.7 x 107km

Earth How far is it between Earth and the other planets in our solar system?

Saturn

1,517,000,000km = 1.517 x 109km

Earth

Uranus

1,747,200,000km = 1.7472 x 109km

Standard Form (Scientific Notation) Changing from Scientific Notation back to "Normal" form

6.28 x 10

5

Write down the 628 without the decimal point

628

Move the point 5 places to the right

628000 5

6.28 x 10 = 628000

Standard Form (Scientific Notation) Changing from Scientific Notation back to "Normal" form

8

3 x 10 = 300,000,000m/s Speed of light

5

3.844 x 10 = 384,400Km Distance to moon

1.496 x 108 = 149,600,000Km Distance to sun

Standard Form (Scientific Notation) It is also possible to write very small numbers Hydrogen Atom

Size of an atomic nucleas

Diameter?

Wavelength of Light

Science Stuff Size of computer components

Standard Form (Scientific Notation) It is also possible to write very small numbers Hydrogen Atom

0.00000000005m Diameter?

0.0000000000000071m

Size of an atomic nucleas

Standard Form (Scientific Notation) Writing numbers in a more compact way

1 = 10-1 10 1 1 -2 = = 10 100 10x10 1 1 -3 = = 10 10x10x10 1000 1 1 -4 = = 10 10x10x10x10 10000 We can use this technique to help us with all small numbers

Standard Form (Scientific Notation) Writing numbers in a more compact way

0.03 = 3 ÷ 100 = 3 x 10-2 0.004 = 4 ÷ 1000 = 4 x 10-3

0.0007 = 7 ÷ 10000 = 7 x 10-4

0.00009 = 9 ÷ 100000 = 9 x 10-5 0.000002 = 2 ÷ 1000000 = 2 x 10-6 We can use this technique to help us with all small numbers

Standard Form (Scientific Notation) A quick way to change to standard form(scientific notation)

0.00468 Move the decimal point to after the first non zero digit

4 68

Count how many places you moved the point Use this number as the negative power of 10

0.00468 = 4.68 x 10

­3

Standard Form (Scientific Notation) Can we now write these in scientific notation?

Hydrogen Atom

Diameter?

0.00000000005m ­11 = 5 x 10 m

Size of an atomic nucleas

0.0000000000000071m ­15

Wavelength of green light

= 7.1 x 10

m

0.000000552m ­7 = 5.52 x 10 m

Standard Form (Scientific Notation) Changing from Scientific Notation back to "Normal" form

­4

8.62 x 10

Write down the 862 with 4 zeros in front Insert the decimal point after the first zero

0000862

0000862

­4

8.62 x 10 = 0.000862

Standard Form (Scientific Notation) Changing from Scientific Notation back to "Normal" form Weight of a steak pie

4.5 x 10

­1

Kg = 0.45Kg 1

Years in a second

­8

3.17 x 10 = 0.0000000317 yrs

yrs

8

Time taken for light

­9 2.98 x 10 s to travel 1m

= 0.00000000298s 9

Standard Form (Scientific Notation) Using a Calulator with Scientific Notation

5.5 E06 means 5.5 x 106 You type

5.5 E06

5.5

EXP

6 =

or

5.5 x 10 ^ 6 = yx

Standard Form (Scientific Notation) Buttons you might need

5.5 E06

Standard Form (Scientific Notation) We can now do more complex calculations with the calculator

6.2 x (4.38 x 104) 5.5 E06

6.2 x 4.38

EXP

4

= 271560

(7.89 x 103) ÷ 8.5 7.89 EXP 3 ÷ 8.5 = 928.24 (3.47 x 104) x (4.26 x 107) 3.47

EXP

4 x 4.26

EXP

7 = 1.48 x 1012

Attachments

ACDC_Highway_To_Hell.mp3 mc1.mp3 Trex11.mp3