Download Standard Form for small numbers

Very large numbers!
BOOM!
How far?
92 000 000 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
Standard Form
When writing a number in
standard form / scientific notation
it must be in the form :
n
a x 10
Where ‘a’ MUST be greater than 1 and less than 10
3
i.e 4.2 x 10
A short cut
8 000 000
Step 1: Put a decimal point at the end of the number
8 000 000.
Step 2:Move the decimal point to get a number between 1 and 10
8. 000 000.
Step 3: Write the number in standard form / scientific notation
8 000 000  8 10
Between 1 and 10
6
The point
moved 6 places
A short cut
92 000 000
Step 1: Put a decimal point at the end of the number
92 000 000.
Step 2:Move the decimal point to get a number between 1 and 10
92
. 000 000.
Step 3: Write the number in standard form / scientific notation
92 000 000  9.2 10
Between 1 and 10
7
The point
moved 7
places
A short cut
228 000 000
Step 1: Put a decimal point at the end of the number
228 000 000.
Step 2:Move the decimal point to get a number between 1 and 10
. 000 000.
228
Step 3: Write the number in standard form / scientific notation
228 000 000  2.28 10
8
Between 1 and 10
The point
moved 8
places
Standard Form
(1) 30 000
 3 1045
(2) 700 000
 7 10 3
(3) 5 300
 5.3 10
5
(4) 470 000
 4.7 106
(5) 9 500 000
 9.5 107
(6) 18 300 000
 1.83 10
5
(7) 329 000
 3.29 10
6
(8) 2 560 000
 2.56 10
(9) 12 000 000 000  1.2 1010
6
(10) 9 990 000
 9.99 10
Changing back
The point
moves 7
places
8.6  10 8.60000000
. =86 000 000
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
3.46  10  3.4600000
. =346 000
5
Hint:
Add 5 zeros, although you
probably won’t need them all.
Zeros after the
point aren’t needed.
Changing back
(1) 6  105
(2) 8 103
(3) 6.5 105
(4) 1.2 108
(5) 3.71106
(6) 3.3 104
(7) 7.91106
(8) 5.55 107
(9) 1.05 104
(10) 3.033 109
= 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
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  10-10metres wide
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.
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.
Standard Form
for small numbers
4
(1) 0. 000 3
 3 10 5
(2) 0.000 07
 7 10
4
(3) 0.000 45
 4.5 103
(4) 0.003 4
 3.4 10
(5) 0. 000 724
 7.24 104
7
(6) 0.000 000 494
 4.94 10
5
(7) 0.000 095
 9.5 108
(8) 0.000 000 098
 9.8 10
4
(9) 0.000 1 03
 1.03 1010
(10) 0.000 000 000 66  6.6 10
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.
2  10  000
-3
= 0.002
Changing back small numbers
-5 so remember to
move point left for
small numbers.
Hint:
Add 5 zeros to the left of the
number.
8.6
.
8.6  10  00000
-5
= 0.000 086
Changing back small numbers
Hint:
-6 so remember to
move point left for Add 6 zeros to the left of the
number.
small numbers.
5.16
5.16  10  000000
.
-6
= 0.000 00516
Changing back small numbers
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
4
= 0.000 5
9 105 = 0.000 09
3
5.8 10 = 0.005 8
7
6.2 10 = 0.000 000 62
6.45 106 = 0.000 006 45
5.3 107 = 0.000 000 53
6 = 0.000 009 17
9.17 103
2.12 10 = 0.002 12
5
2.03 10 = 0.000 020 3
9
6.032 10 = 0.000 000 006 032
5 10