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