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What is Standard Form?
It is a convenient way of writing large or
small numbers.
To write numbers in Standard Form we need
to know how to write the powers of 10.
Standard Form is very useful to scientists
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1=
10 =
100 =
1000 =
10000 =
100000 =
100
101
102
103
104
105
Powers of 10
Now we look at some examples:
800 =
3000 =
45000 =
8 x 100
= 8 x 102
3 x 1000
= 3 x 103
4.5 x 10000
852000 = 8.52 x 100000
1700000 =
= 4.5 x 104
= 8.52 x 105
1.7 x 1000000 = 1.7 x 106
© T Madas
A number is written in standard form when:
a number between
1 and 10
6.4 x 10
4
a power of 10
Now we look at some examples:
800 =
3000 =
45000 =
8 x 100
= 8 x 102
3 x 1000
= 3 x 103
4.5 x 10000
852000 = 8.52 x 100000
1700000 =
= 4.5 x 104
= 8.52 x 105
1.7 x 1000000 = 1.7 x 106
© T Madas
A number is written in standard form when:
a number between
1 and 10
6.4 x 10
4
a power of 10
Which of the following numbers is not written
in standard form?
3
6 x 10
3.07 x 105
8.5 x 109
15 x 104
3.7 x 106
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Practice Writing Numbers in Standard Form
5 0 0 0 0 = 5 x 104
6 2 0 0 0 0 = 6.2 x 105
4 3 7 5 0 0 0 = 4.375 x 106
6 0 0 5 0 0 0 = 6.005 x 106
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Practice Writing Numbers in Standard Form
7 0 = 7 x 101
5 2 7 8 = 5.278 x 101
1 2 5 0 0 5 = 1.25005 x 10
8 = 8 x 10
3
0
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Why does this conversion method work?
5 0 0 0 0 = 5 x 10
Moving 4 d.p.
Divides by 10000
4
We need to multiply by
10000 = 104, so we do
not change the number
10000 = 104
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Converting from Standard form to decimal form
3.3 x 105 = 3.3 x 100000 = 330000
7.25 x 104= 7.25 x 10000 = 72500
3.03 x 102 = 3.03 x 100 = 303
6.5 x 106 = 6.5 x 1000000 = 6500000
© T Madas
Writing Small Numbers
in Standard Form
© T Madas
Writing Small Numbers in Standard Form
0 0 0 0 2 = 2 x 10-4
0 0 0 0 8 4 = 8.4 x 10-4
0 0 0 0 0 1 5 = 1.5 x 10-5
0 0 1 2 5 = 1.25 x 10-2
© T Madas
Why does this conversion method work?
0 0 0 0 5 = 5 x 10
-4
We need to divide by 10000 = 104
Moving 4 d.p.
or multiply by
1
10000
=
1
104
= 10-4
multiplies by 10000
10000 = 104
© T Madas
Standard Form is a convenient way of writing
large or small numbers.
6
6 spaces
Small:
Power of 10
7541000 = 7.541 x 10
Number
between
1 and 10
Large:
0.0027 = 2.7 x 10
-3
3 spaces
© T Madas
© T Madas
2E6
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Ans
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=
© T Madas
1
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hyp
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EXP
Ans
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© T Madas
3E-5
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EXP
Ans
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=
© T Madas
1
1
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2- 3E
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sin
cos
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x3
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hyp
STO
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2
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(
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,
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tan
M- M
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8
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5
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1
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–
3
EXP
1
0
=
Calculate
12
10
5 x 10 – 3 x 10
Answer:
12
4.97 x 10
4 970 000 000 000
=
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3 ÷ 5 20
1
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Ans
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.
3
÷
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=
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hyp
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03
x10
AC
Calculate
1.3 ÷ 520
Answer:
-3
2.5 x 10
0.0025
=
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© T Madas
Standard Form and Negative Numbers
The procedure is the same except that we place a
minus (-) in front of the whole number:
-6000 = -6 x 103
-52000 = -5.2 x 104
-0.0025 = -2.5 x 10-3
-0.00091 = -9.1 x 10-4
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Formally:
Every number except zero can be
written in the form:
± a´
±n
10
where 1 £ a < 10
n = 0, 1, 2, 3, ...
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© T Madas
Practice
On
Standard Form
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Write these Numbers in Standard Form
35000 = 3.5 x 104
5800000 = 5.8 x 106
42500 = 4.25 x 104
101000 = 1.01 x 105
6200 = 6.2 x 103
170000000 = 1.7 x 108
117000 = 1.17 x 105
10350000 = 1.035 x 107
825000 = 8.25 x 105
753000 = 7.53 x 105
3850 = 3.85 x 103
53200000 = 5.32 x 107
990000 = 9.9 x 105
2000000000 = 2 x 109
624 = 6.24 x 102
20 = 2 x 101
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Write these Numbers in Standard Form
41000 = 4.1 x 104
4500000 = 4.5 x 106
356000 = 3.56 x 105
101010 = 1.0101 x 105
1200 = 1.2 x 103
110000000 = 1.1 x 108
1700000 = 1.7 x 106
90800000 = 9.08 x 107
15000 = 1.5 x 104
95317 = 9.5317 x 104
896 = 8.96 x 102
22000000 = 2.2 x 107
99999 = 9.9999 x 104
10000000000 = 1 x 1010
25 = 2.5 x 101
8=
8 x 100
© T Madas
Write these Numbers in Standard Form
550000 = 5.5 x 105
1300000 = 1.8 x 106
3500 = 3.5 x 103
2022000 = 2.022 x 106
7200000 = 7.2 x 106
250000000 = 2.5 x 108
517200 = 5.172 x 105
10430000 = 1.043 x 107
19000 = 1.9 x 104
653 = 6.53 x 102
30000000 = 3 x 107
230000000 = 2.3 x 108
99 = 9.9 x 101
500000000000 = 5 x 1011
8224 = 8.224 x 103
2 = 2 x 100
© T Madas
Quick Test
On
Standard Form
© T Madas
Write these Numbers in Standard Form
35000 = 3.5 x 104
5800000 = 5.8 x 106
42500 = 4.25 x 104
101000 = 1.01 x 105
6200 = 6.2 x 103
170000000 = 1.7 x 108
117000 = 1.17 x 105
10350000 = 1.035 x 107
825000 = 8.25 x 105
753000 = 7.53 x 105
3850 = 3.85 x 103
53200000 = 5.32 x 107
990000 = 9.9 x 105
2000000000 = 2 x 109
624 = 6.24 x 102
20 = 2 x 101
© T Madas
Write these Numbers in Standard Form
41000 = 4.1 x 104
4500000 = 4.5 x 106
356000 = 3.56 x 105
101010 = 1.0101 x 105
1200 = 1.2 x 103
110000000 = 1.1 x 108
1700000 = 1.7 x 106
90800000 = 9.08 x 107
15000 = 1.5 x 104
95317 = 9.5317 x 104
896 = 8.96 x 102
22000000 = 2.2 x 107
99999 = 9.9999 x 104
10000000000 = 1 x 1010
25 = 2.5 x 101
8=
8 x 100
© T Madas
Write these Numbers in Standard Form
550000 = 5.5 x 105
1300000 = 1.8 x 106
3500 = 3.5 x 103
2022000 = 2.022 x 106
7200000 = 7.2 x 106
250000000 = 2.5 x 108
517200 = 5.172 x 105
10430000 = 1.043 x 107
19000 = 1.9 x 104
653 = 6.53 x 102
30000000 = 3 x 107
230000000 = 2.3 x 108
99 = 9.9 x 101
500000000000 = 5 x 1011
8224 = 8.224 x 103
2 = 2 x 100
© T Madas
Practice on writing
Small Numbers
with Standard Form
© T Madas
Write these Numbers in Standard Form
0.00035 = 3.5 x 10-4
0.0000058 = 5.8 x 10-6
0.0425 = 4.25 x 10-2
0.00101 = 1.01 x 10-3
0.000062 = 6.2 x 10-5
0.000000003 = 3 x 10-9
0.00117 = 1.17 x 10-3
0.01035 = 1.035 x 10-2
0.00082 = 8.2 x 10-4
0.000753 = 7.53 x 10-4
0.385 =3.85 x 10-1
0.532 = 5.32 x 10-1
0.0000002 = 2 x 10-7
0.000000011 = 1.1 x 10-8
0.00624 = 6.24 x 10-3
0.003 = 3 x 10-3
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Write these Numbers in Standard Form
0.004 = 4 x 10-3
0.000065 = 6.5 x 10-5
0.000356 = 3.56 x 10-4
0.007 = 7 x 10-3
0.012 =1.2 x 10-2
0.00000008 = 8 x 10-8
0.000017 = 1.7 x 10-5
0.00908 = 9.08 x 10-3
0.00115 = 1.15 x 10-3
0.095317 = 9.5317 x 10-2
0.896 = 8.96 x 10-1
0.00022 = 2.2 x 10-4
0.00009 = 9 x 10-5
0.00000032 = 3.2 x 10-7
0.0017 = 1.7 x 10-3
0.1 = 1 x 10-1
© T Madas
Quick Test on Writing
Small Numbers with
Standard Form
© T Madas
Write these Numbers in Standard Form
0.00035 = 3.5 x 10-4
0.0000058 = 5.8 x 10-6
0.0425 = 4.25 x 10-2
0.00101 = 1.01 x 10-3
0.000062 = 6.2 x 10-5
0.000000003 = 3 x 10-9
0.00117 = 1.17 x 10-3
0.01035 = 1.035 x 10-2
0.00082 = 8.2 x 10-4
0.000753 = 7.53 x 10-4
0.385 =3.85 x 10-1
0.532 = 5.32 x 10-1
0.0000002 = 2 x 10-7
0.000000011 = 1.1 x 10-8
0.00624 = 6.24 x 10-3
0.003 = 3 x 10-3
© T Madas
Write these Numbers in Standard Form
0.004 = 4 x 10-3
0.000065 = 6.5 x 10-5
0.000356 = 3.56 x 10-4
0.007 = 7 x 10-3
0.012 =1.2 x 10-2
0.00000008 = 8 x 10-8
0.000017 = 1.7 x 10-5
0.00908 = 9.08 x 10-3
0.00115 = 1.15 x 10-3
0.095317 = 9.5317 x 10-2
0.896 = 8.96 x 10-1
0.00022 = 2.2 x 10-4
0.00009 = 9 x 10-5
0.00000032 = 3.2 x 10-7
0.0017 = 1.7 x 10-3
0.1 = 1 x 10-1
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Interpreting Numbers
from
Standard Form
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Write these numbers in their “usual” form
2 x 104 = 20,000
4 x 105 = 400,000
5.5 x 104 = 55,000
2 x 106 = 2,000,000
3.1 x 103 = 3,100
6.11 x 102 = 611
8.5 x 105 = 850,000
7.25 x 104 = 72,500
1.22 x 104 = 12,200
6.05 x 106 = 6,050,000
2.4 x 104 = 24,000
4.32 x 106 = 4,320,000
1.728 x 105 = 172,800
2.44 x 103 = 2,440
7 x 108 = 700,000,000 3.125 x 107 = 31,250,000
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Write these numbers in their “usual” form
3 x 104 = 30,000
7 x 105 = 700,000
6.23 x 103 = 6,230
5.05 x 105 = 505,000
3.22 x 104 = 32,200
9.85 x 106 = 9,850,000
3.6 x 104 = 36,000
3.5 x 104 = 35,000
1.15 x 106 = 1,150,000
2.01 x 102 = 201
7.125 x 104 = 71,250
8. 2 x 107 = 82,000,000
1.25 x 105 = 125,000
7.44 x 104 = 7,440
3.25 x 108 = 325,000,000 3.002 x 107 = 30,020,000
© T Madas
Quick Test on
Writing Numbers
from
Standard Form
© T Madas
Write these numbers in their “usual” form
2 x 104 = 20,000
4 x 105 = 400,000
5.5 x 104 = 55,000
2 x 106 = 2,000,000
3.1 x 103 = 3,100
6.11 x 102 = 611
8.5 x 105 = 850,000
7.25 x 104 = 72,500
1.22 x 104 = 12,200
6.05 x 106 = 6,050,000
2.4 x 104 = 24,000
4.32 x 106 = 4,320,000
1.728 x 105 = 172,800
2.44 x 103 = 2,440
7 x 108 = 700,000,000 3.125 x 107 = 31,250,000
© T Madas
Write these numbers in their “usual” form
3 x 104 = 30,000
7 x 105 = 700,000
6.23 x 103 = 6,230
5.05 x 105 = 505,000
3.22 x 104 = 32,200
9.85 x 106 = 9,850,000
3.6 x 104 = 36,000
3.5 x 104 = 35,000
1.15 x 106 = 1,150,000
2.01 x 102 = 201
7.125 x 104 = 71,250
8. 2 x 107 = 82,000,000
1.25 x 105 = 125,000
7.44 x 104 = 7,440
3.25 x 108 = 325,000,000 3.002 x 107 = 30,020,000
© T Madas
© T Madas