Scientific Notation
S t u d e nt
Book - Series J-1
3 x 107
2 x 10-5
Mathletics
Instant
Workbooks
Copyright ©
Scientific notation
Student Book - Series J
Contents
Topics
Date completed
Topic 1 - Powers of 10
__/__/__
Topic 2 - Calculating with powers of 10
__/__/__
Topic 3 - Numbers greater than one
__/__/__
Topic 4 - Numbers less than one
__/__/__
Topic 5 - Scientific notation calculations
__/__/__
Topic 6 - Comparing numbers in scientific notation
__/__/__
Practice Tests
Topic 1 - Topic test A
__/__/__
Topic 2 - Topic test B
__/__/__
Author of The Topics and Topic Tests: AS Kalra
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
CHAPTER 5
ScientificNotation
notation
Scientific
Topic 1: Powers of 10
QUESTION 1
EXCEL INTERMEDIATE MATHS YEARS 9–10
page 23
UNIT 1: Powers of 10
Write the value of the following.
a
10 3 = ______________
b
10 2 = ______________
c
10 4 = ______________
d
10 6 = ______________
e
10 5 = ______________
f
10 7 = ______________
g
10 8 = ______________
h
10 1 = ______________
i
10 9 = ______________
j
10 0 = ______________
k
10 10 = ______________
l
10 11 = ______________
QUESTION 2
Write the following as a power of 10.
a
10 = ______________
b
1000 = ______________
c
100 = ______________
d
10 000 = ______________
e
1 = ______________
f
100 000 = ______________
g
1000 000 = _____________
h
10 000 000 = ____________
i
1 000 000 000 = __________
j
100 000 000 = _____________ k
10 000 000 000 = ____________ l
1 000 000 000 000 = _______
QUESTION 3
Write the following as a basic numeral.
a
2 10 3 = ______________
b
3 10 7 = ______________
c
4 10 2 = ______________
d
5 10 6 = ______________
e
8 10 4 = ______________
f
7 10 1 = ______________
g
9 10 5 = ______________
h
6 10 7 = ______________
i
5 10 10 = ______________
j
3 10 8 = ______________
k
9 10 9 = ______________
l
7 10 11 = ______________
QUESTION 4
Write the following as a fraction.
a
10 –1 = ______________
b
10 –4 = ______________
c
10 –3 = ______________
d
10 –2 = ______________
e
10 –7 = ______________
f
10 –5 = ______________
g
0·1 = ______________
h
10 –6 = ______________
i
0·01 = ______________
j
0·002 = ______________
k
0·0005 = ______________
l
0·001 = ______________
QUESTION 5
Write the following in decimal form.
a
10 –1 = ______________
b
10 –8 = ______________
c
10 –2 = ______________
d
10 –5 = ______________
e
10 –4 = ______________
f
10 –7 = ______________
g
10 –3 = ______________
h
10 –9 = ______________
i
10 –10 = ______________
j
10 –11 = ______________
k
10 –12 = ______________
l
10 –6 = ______________
QUESTION 6
Write the following using powers of 10.
a
30 000 = ______________
b
7000 = ______________
c
500 = ______________
d
10 = ______________
e
100 = ______________
f
8 000 000 = ______________
g
400 000 = ______________
h
60 000 = ______________
i
20 000 000 = ____________
j
0·1 = ______________
k
0·01 = ______________
l
0·0001 = ______________
44
EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
1
Scientific Notation
Scientific notation
UNIT 2: Calculating with powers of 10
Topic 2: Calculating with powers of 10
Give your answer in index notation for questions 1 to 5.
QUESTION 1 Simplify the following.
a
103 104 = ______________ c
106 102 = _____________
105 107 = ______________ h
108 101 = ______________ i
103 105 101 = ________
108 101 = ______________
c
107 104 = _____________
106 102 = ______________
i
1018 107 105 = _______
107 103 = ______________ e
j
105 106 102 = _________ k
Simplify the following.
QUESTION 2
a
107 102 = ______________
g
105 103 101 = _________ h
d
j
10 10 = ______________
d
g
j
(102 )2
d
e
Simplify the following.
109 103 = ______________
f
109 1010 = ____________
1014 103 = ____________
109 102 103 = ________
l
109 106 = _____________
(107 )1 = ______________
c
(1010 )4 = ______________
(103 )8 = ______________
h
(108 )3 = ______________
i
l
106 = ______________
3 12
10 = ______________
c
(108 ) 4 = ______________
i
(1012 ) 2 105 = __________
l
(10 2 ) 5 100 = ___________
108 104 107 = ________
c
108 105 103 = ________
1018
= _____________
104
f
(107 )4 100 = ___________
1020
(105 )3 = ______________
1
2
(104 ) = ______________
1
3
1
3
e
k
Simplify the following.
10 10 = ______________
3
(105 )– 5 = ______________
b
e
10–2 104 = _____________ h
j
(10 5 ) 6 100 = ____________ k
6 10
a
(104 )6
1012
d
(105 )4 1016 = ___________ e
g
(104 )3 108 = ____________ h
(104 )5
j
10 4 10 4 10 4 = __________ k
10–5 = ___________ b
1
1
QUESTION 6
3
1
3
(109 ) = ______________
1
(1024 ) 4 = ______________
1
(1000) 3 = ______________
1
(1 000 000) 3 = ___________
( ) = __________
2
1077
(103 ) 3 10
1044
10
2
3
a
g
105 102 = 10x ___________ h
1 = 10x = ______________ k
10–3
10x
108
f
f
(109 )3 (1013 )2 = __________ i
( )
6 2
(103 )8 10–2 = _________ l
10
Find the value of x in the following.
105
=
(106 )5 = ______________
(1014 )6 = ______________
5
(10 000)4 = ______________
3
1
5
2
Simplify the following.
QUESTION 5
j
108 103 101 = _________ l
109 104 = _____________
b
g
d
108 102 101 = _________ f
= ______________
QUESTION 4
a
b
1015 1010 106 = ________ k
QUESTION 3
a
pages 23–24
102 105 = ______________ b
d
g
EXCEL INTERMEDIATE MATHS YEARS 9–10
______________
b
107 = 10–x = ______________ e
( )
8
(103 )4 102
10
1
3
= ________
1018 108 106 = _______
10–5 = 10x ______________
c
10–8 = 104x ____________
109 103 = 10x __________
i
109 10–4 = 10x _______
106 = 10–x ______________
104 = 10–x ______________
f
l
10–21 = 10x ____________
1012 107 = 10–x ______
45
Chapter 5: Scientific Notation
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
2
Scientific Notation
Scientific notation
EXCEL INTERMEDIATE MATHS YEARS 9–10
page 75
Numbers greater than one
Topic 3: Numbers greaterUNIT
than 3:
one
QUESTION 1
Express each number in scientific notation.
a
32 000 = 3·2 ___________
b
64 000 000 = 6·4 _________ c
93 000 = 9·3 ___________
d
938 000 = 9·38 __________
e
7 500 000 = 7·5 __________ f
630 000 = 6·3 __________
g
6 540 000 = 6·54 _________ h
2 530 000 = _________ 106
8 900 000 = 8·9 _________
j
4160 = ____________ 103
23 700 000 = _________ 107 l
QUESTION 2
k
i
630 000 = _________ 105
Express each number in scientific notation.
a
4800 = ______________
b
80 000 = ______________
c
658 000 = ______________
d
3 250 000 = ______________
e
6 000 000 = ______________
f
539·8 = ______________
g
563 000 = ______________
h
853 000 000 000 = __________ i
j
640 = ______________
k
7935 = ______________
QUESTION 3
4 000 000 = ______________
l
63 000 = ______________
Write each number in scientific notation.
a
893 = ______________
b
300 000 = ______________
c
90 000 = ______________
d
480 000 = ______________
e
63 700 = ______________
f
5 431 000 = _____________
g
639 000 = ______________
h
48 600 000 = _____________
i
39 000 000 = ____________
j
500 000 000 = ___________
k
43·49 = ______________
l
7631·7 = ______________
QUESTION 4
Express each number in scientific notation.
a
9·7 = ______________
b
8·0 = ______________
c
5·38 = ______________
d
7·9 = ______________
e
3 = ______________
f
8 · 2 = ______________
g
9·63 = ______________
h
7·25 = _____________
i
4·62 = ______________
j
8·13 = ______________
k
2·54 = ______________
l
9·75 = ______________
QUESTION 5
Write the following as ordinary numerals.
a
3·4 10 4 = ______________
b
9·25 10 6 = _____________
c
8·23 10 6 = ___________
d
8·15 10 6 = _____________
e
7·01 10 7 = _____________
f
5·4 10 3 = ___________
g
6·351 10 4 = ____________
h
4·03 10 4 = _____________
i
3·486 10 4 = ___________
j
5·381 10 5 = ____________
k
9·5 10 4 = _____________
l
7·29 10 5 = ___________
QUESTION 6
Express the following in scientific notation.
a
five hundred _______________ b
eight thousand ____________
c
three million _____________
d
fifteen thousand ___________
e
half a million _____________
f
one hundred thousand ______
g
63 107 = ______________
h
963·4 = ______________
i
631 107 = _____________
j
27 = ______________
k
798 000 = ______________
l
536 104 = _____________
46
EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
3
Scientific Notation
Scientific notation
UNIT 4: Numbers less than one
EXCEL INTERMEDIATE MATHS YEARS 9–10
page 75
Topic 4: Numbers less than one
QUESTION 1
Express each number in scientific notation.
a
0·0025 = 2·5 ___________
b
0·007 = 7 ____________
c
0·000 018 = 1·8 ________
d
0·0083 = 8·3 ___________
e
0·000 007 2 = 7·2 ________
f
0·0039 = 3·9 __________
g
0·0057 = 5·7 ___________
h
0·0048 = _________ 10–3
i
0·000 071 = _______ 10–5
j
0·0436 = ___________ 10–2 k
0·000 002 2 = _______ 10–6 l
0·000 05 = ________ 10–5
QUESTION 2
Express each number in scientific notation.
a
0·43 = ______________
b
0·008 9 = ______________
c
0·00065 = ______________
d
0·000 41 = ______________
e
0·000 054 9 = ____________
f
0·0736 = ______________
g
0·009 25 = ______________
h
0·003 29 = _____________
i
0·000 000 7 = ___________
j
0·83 = ______________
k
0·000 005 48 = ____________
l
0·0716 = ______________
QUESTION 3
Write each number in scientific notation.
a
0·85 = ______________
b
0·0356 = ______________
c
0·0047 = ______________
d
0·000 831 = ______________
e
0·000 215 = ______________
f
0·008 35 = _____________
g
0·000 17 = ______________
h
0·002 18 = _____________
i
0·000 387 = ____________
j
0·000 000 534 = ___________
k
0·000 123 = ______________
l
0·0005 = ______________
QUESTION 4
Express each number in scientific notation.
a
0·05 = ______________
b
0·008 = ______________
c
0·025 = ______________
d
0·000 006 = ______________
e
0·000 025 1 = ____________
f
0·069 32 = ______________
g
0·000 456 = ______________
h
0·0073 = _____________
i
0·358 = ______________
j
0·000 63 = ______________
k
0·000 084 = _____________
l
0·000 792 = _____________
c
7·6 10 –2 = ___________
QUESTION 5
Write the following as ordinary numerals.
a
5 10 –3 = ______________
d
5·608 10 –4 = ____________ e
5·03 10 –2 = _____________ f
8·3 10 –3 = ___________
g
8·59 10 –4 = ____________
h
5·9 10 –3 = _____________
i
3·33 10 –3 = ___________
j
5·08 10 –3 = ____________
k
9·8 10 –2 = _____________
l
9·61 10 –4 = ___________
c
five-thousandths __________
QUESTION 6
b
8 10 – 6 = _____________
Express the following in scientific notation.
a
three tenths _______________ b
one-hundredth ___________
d
twelve-hundredths __________ e
three-millionths ____________ f
nine-tenths ______________
g
five-hundredths ____________ h
six-millionths _____________
i
seven-tenths _____________
j
0·005 ______________
0·023 ______________
l
0·000 08 _____________
k
47
Chapter 5: Scientific Notation
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
4
Scientific Notation
Scientific notation
EXCEL INTERMEDIATE MATHS YEARS 9–10
page 76
UNITcalculations
5: Scientific notation calculations
Topic 5: Scientific notation
QUESTION 1
Simplify the following, giving your answers in scientific notation.
a
(4 105 ) (3·5 104 ) = __________________ b
(6·7 104 ) (4·2 102 ) = ________________
c
(8·32 107 ) (5·2 103 ) = ________________ d
(3·6 104 ) (5·2 102 ) = ________________
e
(4·9 104 ) (5·8 106 ) = _________________ f
(6·9 105 ) (4·2 108 ) = ________________
QUESTION 2
Express your answers to the following in scientific notation.
a
(8·4 108 ) (2·1 106 ) _________________
b
(6·5 1012 ) (1·3 107 ) _________________
c
(9·6 109 ) (1·6 104 ) _________________
d
(6·3 1020 ) (2·4 1017 ) ________________
e
(9·6 107 ) (4·8 102 ) _________________
f
(2·24 10–8 ) (3·2 105 ) ________________
QUESTION 3
Simplify the following, giving your answers in scientific notation.
a
(6·3 108 ) (2·1 105 ) _________________
b
(3·24 1012 ) (2·4 108 ) _______________
c
(5·86 109 ) (3·5 104 ) _________________
d
(6·4 10–3 )2 _________________
e
(8·9 10–3 )4 _________________
f
9·8 10–7 _________________
1·4 10–5
QUESTION 4
Simplify the following, expressing your answers in scientific notation correct to four
significant figures.
a
58 000 632 000 = ________________________ b
c
8·2 9 236 000 = ________________________
e
(9·2 1032 ) + (1·6 1029 ) = ________________ f
QUESTION 5
d
59 000 5 31 000 = ____________________
70 630 250 480_____________________
3
6·15 1012 = ________________________
Express your answers to the following in scientific notation.
a
(8 105 )4 = ________________________
c
(9·3 106 ) (3·1 10–4 ) = ________________ d
(8 106 ) (3 102 )4 = ________________
e
(7·2 104 ) (1·8 10–3 ) = ________________ f
(8·4 107 ) (2·1 10–6 ) = ______________
QUESTION 6
b
(6 10–4 )2 = ________________________
The following numbers are not in scientific notation. Convert them to scientific notation.
a
847·6 104 = ________________________
b
0·000 072 105 = _____________________
c
85 10–4 = ________________________
d
536·48 10–2 = ______________________
e
1000 10–5 = ________________________
f
0·635 10–4 = _______________________
48
EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
5
Scientific Notation
Scientific
notation
UNIT 6: Comparing numbers in scientific notation
EXCEL INTERMEDIATE MATHS YEARS 9–10
pages 75–76
Topic 6: Comparing numbers in scientific notation
QUESTION 1
Choose the larger number from each pair.
QUESTION 2
Select the smaller number from each pair.
QUESTION 3
Write each group of numbers in ascending order (from smallest to largest).
QUESTION 4
Write each group of numbers in descending order (from largest to smallest).
a
c
e
a
c
e
a
b
c
d
e
f
a
b
c
d
e
f
5 107 or 7 107 __________________
9·8 100 or 3·2 106 __________________
4·8 10–3 or 5·1 10–4 __________________
108
6·2 or 9·3 106 __________________
8·9 104 or 3·2 108 __________________
8·35 10–6 or 8·6 102 __________________
3·5 106 , 3·5 10–8 , 3·5 104
5 10–7 , 5 10–6 , 3 10–2
7 10–3 , 7 10–8 , 7 10–5
3·8 106 , 2·5 104 , 3·1 108
3·8 10–3 , 3·9 10–3 , 5·4 10–3
3·8 103 , 4·9 104 , 3·5 10–5
8
105 ,
8 104 , 8 103
5
7
6
10–3 ,
5
_____________________________________________________
103
4
_____________________________________________________
10–3
9·1 10–2 , 8·3 10–3 , 5·6 10–4
QUESTION 5
a
8
10–3 ,
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
_____________________________________________________
2·1 106 , 1·5 106 , 3·2 106
103 ,
_____________________________________________________
_____________________________________________________
Write the following in the order indicated.
7 103 , 7 102 , 7 104 (smallest to largest)
106 ,
104 ,
102
b
2·3 d
6·8 10–2 , 5·8 10–1 , 4·3 10–3 (largest to smallest)
c
e
f
8·6 3·6 10–2 ,
3·6 8·9 10–1 ,
2·4 (largest to smallest)
10–3
3·2 10–6 ,
105 ,
4·7 10–4 ,
6·5 10–5
____________________________________
____________________________________
(smallest to largest)
____________________________________
____________________________________
9·5 103 , 8·6 103 , 7·8 103 (ascending order)
QUESTION 6
a
b
c
d
e
f
6·03 100 or 6·03 10–2 _________________
5·9 10–6 or 3·1 10–4 __________________
7·5 10–5 or 8·9 103 __________________
b
d
f
_____________________________________________________
5·3 104 , 3·9 105 , 7·6 103
103 ,
6·4 105 or 2·5 104 __________________
5 10–2 or 6 10–5 __________________
4·8 10–3 or 6·7 102 __________________
b
d
f
____________________________________
(descending order)
____________________________________
Select the largest number from each group.
6·3 5·8 10–3 , 3·7 105
6·2 109 , 6·2 108 , 6·2 104
8 104 , 8 105 , 8 10–7
1·3 103 , 1·3 106 , 1·3 109
4·5 10–6 , 4·5 10–4 , 4·5 10–2
9·3 109 , 9·3 107 , 9·3 105
__________________
__________________
__________________
__________________
__________________
__________________
49
Chapter 5: Scientific Notation
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
6
Maths Revision Yr 9 Part 1.qxd:2717_0108R1_pp01_98.qxd
21/2/08
6:39 PM
Page 50
Scientific notation
TOPICTest
TEST
Topic
PARTAA
PART
Scientific
Notation
Time allowed: 15 minutes
Total marks = 15
Time allowed: 15 minutes
1
Write the value of
A 5 10
100 000
D
None of these
1
Write 1 000 000 as a power of 10.
A 107
B 106
C
105
D
104
1
Write 5 103 as a basic numeral.
A 5 3 10
B 5 100
C
5 1000
D
5000
1
C
1
1000
D
1000
1
Write 10–5 in decimal form.
A 0·001
B 0·0001
C
0·000 01
D
0·000 001
1
Write 6 104 as an ordinary numeral.
A 6 4 10
B 6 1000
C
6 10 000
D
60 000
1
1 with negative index.
(103 )4
10–3
B 10–4
C
10–7
D
10–12
1
Simplify 1012 105 103 .
A 1020
B 1012
C
1010
D
104
1
4·05 10–6 equals
A 0·000 040 5
B
C
40 500
D
4 050 000
1
3
Write 10–3 as a fraction.
A
1
B 1
30
300
5
6
7
Write
A
8
9
10 000
4
B
0·000 004 05
10 Which one of the following numbers is written in scientific notation?
A
8 10 000
B
80 000
11 (3 105 ) (6 10–3 ) equals
A
5 103
B
50 000
12 Express 8 million in scientific notation.
A
8 104
B
8 105
13 Express 0·0059 in standard notation.
A
59 101
B
59 102
14 Write 7 10–6 as ordinary numerals.
A
0·0007
B
0·000 07
C
8 104
D
80 103
1
C
5 107
D
5 108
1
C
8 106
D
8 107
1
C
5·9 10–3
D
5·9 104
1
C
0·000 007
D
0·000 000 7
1
D
3·6 10–8
1
15 Simplify (6 10–4 )2 giving your answer in scientific notation.
A
6 10–2
B
6 10–8
C
3·6 10–7
Total marks for PART A
Total marks achieved for PART A
50
Marks
C
2
105 .
Total marks = 15
Scientific notation
15
15
7
EXCEL ESSENTIAL SKILLS: YEAR 9 MATHEMATICS REVISION AND EXAM WORKBOOK 1
Mathletics Instant Workbooks – Series J Copyright © 3P Learning
Maths Revision Yr 9 Part 1.qxd:2717_0108R1_pp01_98.qxd
21/2/08
6:39 PM
Page 51
Scientific notation
TOPIC
TEST
Topic
Test
PARTB B
PART
Scientific Notation
Time allowed: 15 minutes
Total marks = 15
Time allowed: 15 minutes
Total marks = 15
Marks
Question 1
a
1
(108 ) 2
1
3
1
___________________________
1
b
(106 )
c
109 107 105
___________________________
1
d
1015 109 106
___________________________
1
___________________________
1
e
4
3
100
___________________________
4
3
10 10 10
4
3
Question 2
a
Find the value of x in 1018 1012 = 10x .
___________________________
1
b
Express 17 000 in scientific notation.
___________________________
1
c
Write 0·00005 in scientific notation.
___________________________
1
d
Express 596 10–4 in scientific notation.
___________________________
1
e
Write 1·5 103 as a basic numeral.
___________________________
1
One astronomical unit is about 149 000 000 km.
Write this in scientific notation.
________________________________________________
___________________________
1
b
Write 4·3 106 , 4·3 104 , 4·3 103 in ascending order.
________________________________________________
___________________________
1
c
Simplify (6·8 106 ) (2·8 10–3 ) in scientific notation.
________________________________________________
___________________________
1
d
Convert 0·000 007 109 to scientific notation.
________________________________________________
___________________________
1
e
Express the number of centimetres in 370 km in scientific
notation.
________________________________________________
___________________________
1
Question 3
a
Total marks for PART B
Total marks achieved for PART B
Chapter 5: Scientific Notation
Scientific notation
Mathletics Instant Workbooks – Series J
Copyright © 3P Learning
15
15
8
51