Negative Powers of ten · Powers of ten Small answers Powers Negative powers Scienti c Notation The Quick Way Your Turn In reverse Examples Your Turn Small answers Write the following

NegativePowers of ten

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Negative powers

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Negative Powers of ten


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Negative powers

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Write the following as a fraction and a decimal:

(a) 1÷ 2

= 12 = 0.5

(b) 1÷ 4

= 14 = 0.25

(c) 1÷ 8

= 18 = 0.125

(d) 1÷ 16

= 116 = 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4

Dividing a small number by a larger numberalways gives an answer less than one


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(a) 1÷ 2 = 12

= 0.5

(b) 1÷ 4

= 14 = 0.25

(c) 1÷ 8

= 18 = 0.125

(d) 1÷ 16

= 116 = 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4

= 14 = 0.25

(c) 1÷ 8

= 18 = 0.125

(d) 1÷ 16

= 116 = 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14

= 0.25

(c) 1÷ 8

= 18 = 0.125

(d) 1÷ 16

= 116 = 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8

= 18 = 0.125

(d) 1÷ 16

= 116 = 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18

= 0.125

(d) 1÷ 16

= 116 = 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16

= 116 = 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116

= 0.0625

(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116 = 0.0625(e) 2÷ 8

= 28 =14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116 = 0.0625(e) 2÷ 8 = 28

= 14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116 = 0.0625(e) 2÷ 8 = 28 =

14

= 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116 = 0.0625(e) 2÷ 8 = 28 =

14 = 0.25

(f) 8÷ 40

= 840 =25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116 = 0.0625(e) 2÷ 8 = 28 =

14 = 0.25

(f) 8÷ 40 = 840

= 25 = 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116 = 0.0625(e) 2÷ 8 = 28 =

14 = 0.25

(f) 8÷ 40 = 840 =25

= 0.4



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(a) 1÷ 2 = 12 = 0.5(b) 1÷ 4 = 14 = 0.25(c) 1÷ 8 = 18 = 0.125(d) 1÷ 16 = 116 = 0.0625(e) 2÷ 8 = 28 =

14 = 0.25

(f) 8÷ 40 = 840 =25 = 0.4



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Powers

Find the following:

(a) 22

= 4

(b) 23

= 8

(c) 24

= 16


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Powers

Find the following:

(a) 22 = 4

(b) 23

= 8

(c) 24

= 16


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Powers

Find the following:

(a) 22 = 4

(b) 23 = 8

(c) 24

= 16


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Negative powers

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Powers

Find the following:

(a) 22 = 4

(b) 23 = 8

(c) 24 = 16


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Powers

Find the following:

(a) 1÷ 22

= 122

= 14 = 0.25

(b) 1÷ 23

= 123

= 18 = 0.125

(c) 1÷ 24

= 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23

= 123

= 18 = 0.125

(c) 1÷ 24

= 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14

= 0.25

(b) 1÷ 23

= 123

= 18 = 0.125

(c) 1÷ 24

= 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23

= 123

= 18 = 0.125

(c) 1÷ 24

= 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23 = 123

= 18 = 0.125

(c) 1÷ 24

= 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23 = 123

= 18

= 0.125

(c) 1÷ 24

= 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23 = 123

= 18 = 0.125

(c) 1÷ 24

= 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23 = 123

= 18 = 0.125

(c) 1÷ 24 = 124

= 116 = 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23 = 123

= 18 = 0.125

(c) 1÷ 24 = 124

= 116

= 0.0625


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Negative powers

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Powers

Find the following:

(a) 1÷ 22 = 122

= 14 = 0.25

(b) 1÷ 23 = 123

= 18 = 0.125

(c) 1÷ 24 = 124

= 116 = 0.0625


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Negative powers

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Negative Powers

A shorthand way of writing 122

is

2−2

Rewrite the following as fractions, then as a decimal

(a) 2−3

= 123

= 18 = 0.125

(b) 2−4

= 124

= 116 = 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3

= 123

= 18 = 0.125

(b) 2−4

= 124

= 116 = 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4

= 124

= 116 = 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18

= 0.125

(b) 2−4

= 124

= 116 = 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

ScientificNotation

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4

= 124

= 116 = 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


Small answers

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Negative powers

ScientificNotation

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Your Turn

Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

ScientificNotation

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116

= 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2

= 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2 = 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2 = 1102

= 1100

= 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2 = 1102

= 1100 = 0.01

(d) 10−3

= 1103

= 11000 = 0.001


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Negative powers

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Your Turn

Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2 = 1102

= 1100 = 0.01

(d) 10−3 = 1103

= 11000 = 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2 = 1102

= 1100 = 0.01

(d) 10−3 = 1103

= 11000

= 0.001


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Negative powers

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Negative Powers


is 2−2


(a) 2−3 = 123

= 18 = 0.125

(b) 2−4 = 124

= 116 = 0.0625

(c) 10−2 = 1102

= 1100 = 0.01

(d) 10−3 = 1103

= 11000 = 0.001


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Negative powers

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Scientific Notation

This lets us use scientic notation to write very small numbers:

e.g. 0.002

= 2× 0.001 = 2× 11000 = 2×1

103= 2× 10−3

e.g.0.00032

= 3.2× 0.0001 = 3.2× 110000 = 3.2×1

104= 3.2× 10−4


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Scientific Notation


e.g. 0.002 = 2× 0.001

= 2× 11000 = 2×1

103= 2× 10−3

e.g.0.00032

= 3.2× 0.0001 = 3.2× 110000 = 3.2×1

104= 3.2× 10−4


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Scientific Notation


e.g. 0.002 = 2× 0.001 = 2× 11000

= 2× 1103

= 2× 10−3

e.g.0.00032

= 3.2× 0.0001 = 3.2× 110000 = 3.2×1

104= 3.2× 10−4


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Scientific Notation


e.g. 0.002 = 2× 0.001 = 2× 11000 = 2×1

103

= 2× 10−3

e.g.0.00032

= 3.2× 0.0001 = 3.2× 110000 = 3.2×1

104= 3.2× 10−4


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Scientific Notation


e.g. 0.002 = 2× 0.001 = 2× 11000 = 2×1

103= 2× 10−3

e.g.0.00032

= 3.2× 0.0001 = 3.2× 110000 = 3.2×1

104= 3.2× 10−4


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Scientific Notation


e.g. 0.002 = 2× 0.001 = 2× 11000 = 2×1

103= 2× 10−3

e.g.0.00032 = 3.2× 0.0001

= 3.2× 110000 = 3.2×1

104= 3.2× 10−4


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Scientific Notation


e.g. 0.002 = 2× 0.001 = 2× 11000 = 2×1

103= 2× 10−3

e.g.0.00032 = 3.2× 0.0001 = 3.2× 110000

= 3.2× 1104

= 3.2× 10−4


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Scientific Notation


e.g. 0.002 = 2× 0.001 = 2× 11000 = 2×1

103= 2× 10−3

e.g.0.00032 = 3.2× 0.0001 = 3.2× 110000 = 3.2×

1104

= 3.2× 10−4


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Negative powers

ScientificNotation

The Quick Way

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In reverse

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The quick way

To write a decimal number in scientific notation:

Move the decimal point after the first significant figure

Count how many places the decimal point has moved

Write this as a negative power of ten


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Examples- Page 43, Exercise 4, Question 1

Write in scientific notation

(a) 0.008

= 8× 10−3

(b) 0.000067

= 6.7× 10−5

(c) 0.0931

= 9.31× 10−2


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(a) 0.008 = 8× 10−3

(b) 0.000067

= 6.7× 10−5

(c) 0.0931

= 9.31× 10−2


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Negative powers

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(a) 0.008 = 8× 10−3

(b) 0.000067 = 6.7× 10−5

(c) 0.0931

= 9.31× 10−2


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Negative powers

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(a) 0.008 = 8× 10−3

(b) 0.000067 = 6.7× 10−5

(c) 0.0931 = 9.31× 10−2


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Negative powers

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Page 43, Exercise 4

Try Questions 1(c)-(h) & 2


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In Reverse

To convert from scientific notation to full number form:

Move the decimal left by the number in the power of ten

Fill in the spaces with zeros (make sure there is a zerobefore the decimal point!)


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Negative powers

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Page 43, Exercise 4, Question 3

Write the following numbers in full

(a) 3.4× 10−2

= 0.034

(b) 5.7× 10−4

= 0.00057

(c) 6.38× 10−3

= 0.00638


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Negative powers

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(a) 3.4× 10−2 = 0.034(b) 5.7× 10−4

= 0.00057

(c) 6.38× 10−3

= 0.00638


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Negative powers

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(a) 3.4× 10−2 = 0.034(b) 5.7× 10−4 = 0.00057(c) 6.38× 10−3

= 0.00638


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Negative powers

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(a) 3.4× 10−2 = 0.034(b) 5.7× 10−4 = 0.00057(c) 6.38× 10−3 = 0.00638


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Negative powers

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Page 43, Exercise 4

Try Questions 3(d) onwards

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Negative Powers of ten · Powers of ten Small answers Powers Negative powers Scienti c Notation The Quick Way Your Turn In reverse Examples Your Turn Small answers Write the following