Transcript File - Official Mathematics Revision Website

Standard Form
Scientific Notation
Writing large numbers, greater than 10,
in Standard Form
Standard form splits numbers into two parts:
a number between 1 and 10
( 1 ≤ a < 10 )
Multiplied by a number of 10’s
(x10n )
Write the following in Standard form:
a) 381000
= 3·81 x 10 x 10 x 10 x 10 x 10
= 3·81 x 105
Read as 3·81 x 10 to the power 5
The power of 10 tells you how many times the decimal
point must be moved to return to the original number
= 3·81
= 381000·
38· 1
381·
38100·
3810·
b)
9200000 
= 9·2
x
106
d) 72
c) 48350
x 104
=
4·835
e) 500000000
= 5
x
108
= 7·2
x
101
e) 8105
=
8·105
x
103
Express these numbers in Standard Form a x 10n
1. 4 300 4·3 x 103
2. 700 000 7·0 x 105
3. 6 070
4. 18
6·07 x 103
1·8 x 101
5. 211 2·11 x 102
6. 2 740 000 2·74 x 106
7. 55 000
8. 8 780 000 8·78 x 106
5·5 x 104
9. 93 150 000 9·315 x 107 10. 31 570 3·157 x 104
Write these numbers out in full
1. 6·3 x 104
63000
3. 8·01 x 106
8010000
2. 1·18 x 103
1180
4. 4·217 x 104
42170
5. 6 x 107
60000000
6. 9·82 x 102
982
7. 2·4 x 101
24
8. 7·8451 x 103
7845·1
10. 5·562 x 105
9. 3·91 x 107
39100000
556200
Writing small numbers, less than 1, in
Standard Form
Standard form splits numbers into two parts:
a number between 1 and 10
( 1 ≤ a < 10 )
Multiplied by a number of 10’s
(x10n )
For small numbers n is negative
Write the following in Standard Form
a) 0 · 00034
= 3·4
x 10-4
c) 0 · 7
= 7
x 10-1
b) 0 · 061 8
= 6·18
x
10-2
d) 0 · 0 0 5 9
= 5·9
x
10-3
Express these numbers in Standard Form a x 10n
1. 0·0041
4·1 x 10-3
3. 0·00017
1·7 x 10-4
5. 0·0000063
6·3 x 10-6
7. 0·03
3 x 10-2
9. 0·000000493
4·93 x 10-7
2. 0·529
5·29 x 10-1
4. 0·0825
8·25 x 10-2
6. 0·000907
9·07 x 10-4
8. 0·0000288
2·88 x 10-5
10. 0·4917
4·917 x 101
Write these numbers out in full
1. 6·3 x 10-2
0·063
3. 8·01 x 10-6
0·00000801
2. 1·18 x 10-3
0·00118
4. 4·217 x 10-4
0·0004217
5. 6 x 10-7
0·0000006
6. 9·82 x 10-2
0·0982
7. 2·4 x 10-1
0·24
8. 7·8451 x 10-3
0·007845
10. 5·562 x 10-5
9. 3·91 x 10-7
0·000000391
0·00005562
Now do Exercise 12.1
on page 41 in S13
Standard Form
Fourth year revision
Standard Form – revision examples
(Significant figures)
1. Perform each of the calculations below giving your answer
in scientific notation with 3 significant figures 8384
a) 3870 × 2344 b) 3.8 × 106 × 2.67 × 103 c)
0.00456

2. The total mass of gas in a container is 5.89
10-3gms.
Given that the mass of a single atom is 4.56
10-18, find to
3 significant figures the number of atoms in the container.


3. The planet Pluto is at a distance of 1.54 109 kilometers from the earth.
A space rocket travels at 12450 km/hour. How long will it take
the rocket to reach Pluto?
4. A cyclotron is a machine which can produce high speed particles.
A particle moving inside the cyclotron takes 8.3 10-8 seconds
to travel 3.2
10-1 meters. Calculate the speed of the particle in meters per
second.



5. The total number of visitors to the Tower of London last year was 3.45 105.
The exhibition was open each day from 10th June to 14th September inclusive.
Calculate the average number of visitors per day to the exhibition.
6. A planet takes 94 days to travel round the sun.
 Planet

Sun
The path of the planet is a circle with a
diameter of 4.6 1010 kilometers.
Find the speed of the planet as it travels round the sun.
Give your answer in km per hour, correct to 3 significant figures.

7. Large distances in space are measured in ‘light years’.
A camera on a space telescope photographs a galaxy a distance
of 80 million light years away. One light year
is approximately 9.45
1012 kilometres.
Calculate the distance of the galaxy from the space telescope in kilometers.
Give your answer in scientific notation.


8. The annual profit (₤) of a company was 4.8
108 for the year 2005- 2006
What profit did the company make per second?
Give your answer to 3 significant figures.

9. A jet liner has now flown 12.6 109 miles.
This is equivalent to 324 journeys from the earth to the moon.
Calculate the distance from the earth to the moon.
Give your answer in scientific notation correct to 3 significant figures.
10. The distance from Earth to the nearest star Proxima Centauri is
2.5 × 1013 miles. How long does it take light to travel from this star
to Earth if the speed of light is 1.86 × 105 miles per second?
Give your answer in years.
11. There are 5 × 109 red blood cells in 1 millilitre of blood.
The average person has 5.5 litres of blood. How many red
blood cells does the average person have in their blood?
Give your answer in scientific notation.
12. A spider weighs approximately 19.06 × 10-5 kilograms.
A humming bird is 18 times heavier.
Calculate the weight of the humming bird.
Give your answer in scientific notation.
13. It is estimated that in Britain 10000 biscuits of one kind or another
are eaten every minute. How many are eaten in a year?
Give your answer in scientific notation.