Transcript Standard Form for small numbers

Very large numbers!
BOOM!
How
92
000far?
000 miles
Very large numbers!
Happy 70th Birthday!
SPLAT!
Howyears
many= seconds
in 70
years?
70
2 200 000
000
seconds!
Very large numbers!
Dinosaurs roamed the earth
228 million years ago
Short hand!
10
 10 1
100 = 10 x 10
 10 2
1 000 = 10 x 10 x 10
 10 3
10 000 = 10 x 10 x 10 x 10
 10 4
100 000 = 10 x 10 x 10 x 10 x 10
 10 5
1 000 000 = 10 x 10 x 10 x 10 x 10 x 10
 10 6
Standard Form
200 = 2 x 100
 2  10 2
4 000 = 4 x 1000
 4  10
70 000 = 7 x 10 000
3
 7  10 4
500 000 = 5 x 100 000
 5  10
3 000 000 = 3 x 1 000 000
5
 3  10 6
This is also known as
Scientific Notation.
Exercise 1
(1) 2 000 = 2 x 1000  2  10
3
(2) 20 000 = 2 x 10 000  2  10 4
(3) 500 = 5 x 100  5  10 2
(4) 800 000 = 8 x 100 000  8  10 5
(5) 9 000 000 = 9 x 1 000 000  9  10 6
A short cut
Move the point to get a
number between 1 and 10
8. 000 000.  8  10
Add the
decimal point
Between 1 and 10
6
The point
moved 6 places
A short cut
Move the point to get a
number between 1 and 10
92
. 000 000 .  9.2  10
7
Add the
decimal point
Between 1 and 10
9.2  10 miles
7
The point
moved 7
places
A short cut
Move the point to get a
number between 1 and 10
2. 200 000 000 .  2.2  10
Add the
decimal point
9
The point
moved 9
places
Happy Birthday:Between
2.21 and10
10 Seconds old!
9
SPLAT!
A short cut
Move the point to get a
number between 1 and 10
228
. 000 000. 2.28  10
Add the
decimal point
8
The point
moved 8
places
Between 1 and 10
2.28  10 years ago!
8
Exercise 2
(1) 30 000  3  10 4
5
(2) 700 000  7  10
(3) 5 300  5.3  10 3
5
(4) 470 000  4.7  10
(5) 9 500 000  9.5  10 6
(6) 18 300 000  1.83  10 7
(7) 329 000  3.29  10 5
(8) 2 560 000  2.56  10 6
(9) 12 000 000 000  1.2  10 10
(10) 9 990 000  9.99  10 6
Changing back
The point
moves 7
places
. =86 000 000
8.6  10  8.60000000
7
Hint:
Add 7 zeros, although you
probably won’t need them all.
Zeros after the
point aren’t needed.
Changing back
The point
moves 5
places
. =346 000
3.46  10  3.4600000
5
Hint:
Add 5 zeros, although you
probably won’t need them all.
Zeros after the
point aren’t needed.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
Exercise 3
6  10 5
= 600 000
3
8  10
= 8 000
6.5  10 5
= 650 000
1.2  10 8
= 120 000 000
3.71  10 6 = 3 710 000
3.3  10 4
= 33 000
7.91  10 6 = 7 910 000
5.55  10 7 = 55 500 000
1.05  10 4 = 10 500
3.033  10 9 = 3 033 000 000
Name that number!
3
one thousand
this called?
1 000  1  10 What’s
6
one million
this called?
1 000 000  1  10 What’s
9
one?
one this
billion
1 000 000 000  1  10 and
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
100
000 000 000 000 000 000  1  10
What’s
this called?
one googal
!!!
Very small numbers!
How wide is an atom?
0.000 000 000 1 metres wide!
Standard Form for small numbers
Move the point to get a
number between 1 and 10
0.000 000 000 1 .  1  10
10
The point moved 10
places. Negative sign
for small numbers.
1  10 10 metres wide
Note:
10 zeros at the start!
Standard Form for small numbers
Move the point to get a
number between 1 and 10
.  7.6  10
0.000 000 76
7
The point moved 7
places. Negative sign
for small numbers.
Note:
7 zeros at the start!
Standard Form for small numbers
Move the point to get a
number between 1 and 10
0.000 001. 93  1.93  10
6
The point moved 6
places. Negative sign
for small numbers.
Note:
6 zeros at the start!
Exercise 4
(1) 0. 000 3  3  10 4
5
(2) 0.000 07  7  10
(3) 0.000 45  4.5  10 4
(4) 0.003 4  3.4  10 3
(5) 0. 000 724  7.24  10 4
(6) 0.000 000 494  4.94  10 7
(7) 0.000 095  9.5  10 5
(8) 0.000 000 098  9.8  10 8
(9) 0.000 1 03  1.03  10 4
(10) 0.000 000 000 66  6.6  10 10
Question for each:
How many zeros at the start?
Changing back small numbers
-3 so remember to
move point left for
small numbers.
Hint:
Add 3 zeros to the left of the
number.
2  10  000
. 2.
-3
= 0.002
Changing back small numbers
-3 so remember to
move point left for
small numbers.
8.6  10
-5
Hint:
Add 5 zeros to the left of the
number.
 00000
8.6
.
= 0.000 086
Changing back small numbers
-3 so remember to
move point left for
small numbers.
5.16  10
-6
Hint:
Add 6 zeros to the left of the
number.
 000000
5.16
.
= 0.000 00516
Exercise 5
(1) 5  10 4
= 0.000 5
(2) 9  10 5
= 0.000 09
(3) 5.8  10 3
= 0.005 8
(4) 6.2  10 7
= 0.000 000 62
(5) 6.45  10 6 = 0.000 006 45
(6) 5.3  10 7
= 0.000 000 53
(7) 9.17  10 6 = 0.000 009 17
(8) 2.12  10 3 = 0.002 12
(9) 2.03  10 5 = 0.000 020 3
(10) 6.032  10 9 = 0.000 000 006 032
Question for each:
How many zeros at the start?