Standard Form
26
Presen ts
description
Glasgow Mathematics. Presents. Standard Form. Very large numbers!. BOOM!. How far?. 92 000 000 miles. Happy 70 th Birthday!. How many seconds in 70 years?. Very large numbers!. SPLAT!. 70 years = 2 200 000 000 seconds!. Very large numbers!. - PowerPoint PPT Presentation
Transcript of Standard Form
Presents
Very large numbers!
BOOM!
How far?92 000 000 miles
How many seconds in 70 years?
70 years = 2 200 000 000 seconds!
Very large numbers!
Happy 70th Birthday!
SPLAT!
Dinosaurs roamed the earth 228 million years
ago
Very large numbers!
Short hand!
100 = 10 x 10
1 000 = 10 x 10 x 10
100 000 = 10 x 10 x 10 x 10 x 10
10 000 = 10 x 10 x 10 x 10
1 000 000 = 10 x 10 x 10 x 10 x 10 x 10
10
210310
410510
110
610
Standard Form
200 = 2 x 100
4 000 = 4 x 1000
500 000 = 5 x 100 000
70 000 = 7 x 10 000
3 000 000 = 3 x 1 000 000
21023104
41075105
6103
This is also known as
Scientific Notation.
Exercise 1
(1)2 000
(2) 20 000
(3) 500
(4) 800 000
(5) 9 000 000
= 5 x 100 2105
= 8 x 100 000 5108
= 2 x 10 000 4102
= 9 x 1 000 000 6109
= 2 x 1000 3102
Add the decimal point
A short cut
8 000 000 6108..
Between 1 and 10
The point moved 6 places
Move the point to get a number between 1 and 10
A short cut
92 000 000 71029 ...
Add the decimal point
Between 1 and 10
The point moved 7 places
Move the point to get a number between 1 and 10
miles1029 7.
A short cut
2 200 000 000 91022 ...
Add the decimal point
Between 1 and 10
The point moved 9 places
Move the point to get a number between 1 and 10
Happy Birthday: Seconds old! 91022 .
SPLAT!
A short cut
228 000 000 8102.28..
Add the decimal point
Between 1 and 10
The point moved 8 places
Move the point to get a number between 1 and 10
ago! years10282 8.
Exercise 2(1) 30 000(2) 700 000(3) 5 300(4) 470 000(5) 9 500 000(6) 18 300 000(7) 329 000(8) 2 560 000(9) 12 000 000 000(10) 9 990 000
31035 .51074 .
5107
61059 .
4103
710831 .510293 .
610562 .101021 .
610999 .
Changing back
=86 000 000 7108.6
Zeros after the point aren’t needed.
The point moves 7 places
8.60000000.Hint:
Add 7 zeros, although you probably won’t need
them all.
=346 000 5103.46
Zeros after the point aren’t needed.
The point moves 5 places
3.4600000.Hint:
Add 5 zeros, although you probably won’t need
them all.
Changing back
Exercise 3(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
51056 .81021 .
3108
610713 .
5106
41033 .610917 .710555 .410051 .
9100333 .
= 600 000= 8 000= 650 000= 120 000 000= 3 710 000= 33 000= 7 910 000= 55 500 000= 10 500= 3 033 000 000
What’s this called?
What’s this called?
and this one?
What’s this called?
Name that number!
10 000 000 000 000 000 000
000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
000 000 000 000 000 000
100101
1 0001 000 000
1 000 000 000
31016101
9101
one thousand
one million
one billion
one googal !!!
Very small numbers!
How wide is an atom?
0.000 000 000 1 metres wide!
Standard Form for small numbers
0.000 000 000 1 10101 .
The point moved 10 places. Negative sign for small numbers.
Move the point to get a number between 1 and 10
wide metres101 10
Standard Form for small numbers
0.000 000 76 71067 ..
The point moved 7 places. Negative sign for small numbers.
Move the point to get a number between 1 and 10
Standard Form for small numbers
0.000 001 93 610931 ..
The point moved 6 places. Negative sign for small numbers.
Move the point to get a number between 1 and 10
Exercise 4(1) 0. 000 3(2) 0.000 07(3) 0.000 45(4) 0.003 4(5) 0. 000 724(6) 0.000 000 494(7) 0.000 095(8) 0.000 000 098(9) 0.000 1 03(10) 0.000 000 000 66
41054 .31043 .
5107
410247 .
4103
710944 .51059 .
81089 .410031 .
101066 .
Changing back small numbers
= 0.002
-3102 2000.
Hint:Add 3 zeros to the left of
the number.
-3 so remember to move point left for small numbers.
.
Changing back small numbers
= 0.000 086
-5108.6 8.600000.
Hint:Add 5 zeros to the left of
the number.
-3 so remember to move point left for small numbers.
Changing back small numbers
= 0.000 00516
-6105.16 5.16000000.
Hint:Add 6 zeros to the left of
the number.
-3 so remember to move point left for small numbers.
Exercise 5(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)
31085 .71026 .
5109
610456 .
4105
71035 .610179 .310122 .510032 .
9100326 .
= 0.000 5= 0.000 09= 0.005 8= 0.000 000 62= 0.000 006 45= 0.000 000 53= 0.000 009 17= 0.002 12= 0.000 020 3= 0.000 000 006 032
K Hughes 2003
