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Chapter 10

2 a The large cube is made up of 3 3 3 small cubes 2 0 3 0 3 0 3 0 3 x x

Because each small cube contains 3 the total amount Because 0 3 is used as a factor 4 times its exponent is 4

of money in the large cube is 3 3 3 3 34 Because x is used as a factor 2 times its exponent is 2

So 0 3 0 3 0 3 0 3 x x 0 3 x 2

There is 81 in the large cube

3 54 5 5 5 5 625

3 a 1026 100 000 000 000 000 000 000 000 000

The diameter of the observable universe is 1 1 1 1 1

100 000 000 000 000 000 000 000 000 meters 6 6 6 6 216

b 1021 1 000 000 000 000 000 000 000

5 33 27 27 27 1 1

The diameter of the Milky Way Galaxy is

1 000 000 000 000 000 000 000 meters

6 9 25 0 5 9 32 0 5 9 16 7

This can be written as one sextillion meters

c 1016 10 000 000 000 000 000 7 The diameter is 1 8 meters so the radius is 0 9 meter

The diameter of the solar system is Inner sphere V pr

10 000 000 000 000 000 meters 3

This can be written as ten quadrillion meters

d 107 10 000 000

The diameter of Earth is 10 000 000 meters 3

This can be written as ten million meters 0 972p

e 106 1 000 000 9

Outer sphere p 4 5p

The length of the Lake Erie shoreline is 2

1 000 000 meters The volume of the inflated space is

This can be written as one million meters 4 5p 0 972p 3 528p or about 11 08 cubic meters

f 105 100 000 10 1 Exercises pp 414 415

The width of Lake Erie is 100 000 meters Vocabulary and Concept Check

This can be written as one hundred thousand meters

1 34 is the negative of 34 so the base is 3 the exponent

is 4 and its value is 81 3 has a base of 3 an

4 Wives 71

Sacks 7 7 7 2 exponent of 4 and a value of 81

Cats 7 7 7 73 2 The second one does not belong because it is an incorrect

statement about the expression The power is the entire

Kits 7 7 7 7 7 4

expression 53

5 You can use exponents to write the product of repeated

Practice and Problem Solving

Sample answer The formula for the volume of a cube

V s 3 is an example of how exponents are used in real Because 3 is used as a factor 4 times the exponent is 4

life Exponents are also used in measuring astronomical So 3 3 3 3 34

10 1 On Your Own pp 412 413

Because 6 is used as a factor 2 times the exponent is 2

1 So 6 6 6

Because is used as a factor 5 times its exponent is 5

1 1 1 1 1 1

4 4 4 4 4 4

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Chapter 10

1 1 1 17 The negative sign is not part of the base

2 2 2 62 6 6 36

Because is used as a factor 3 times the exponent is 3 18 675

So 5 5 9 3

2 2 2 2 5 5 3 3 3

1 1 1 The prime factorization of 675 is 5 5 3 3 3

3 3 3 or 52 33

Because is used as a factor 3 times the exponent is 3 1 1 1 1

3 3 3 3 Because is used as a factor 4 times the exponent is 4

7 p p p x x x x 1 1 1 1 1

Because p is used as a factor 3 times the exponent is 3 4 4 4 4 4

Because x is used as a factor 4 times the exponent is 4

So p p p x x x x p 3 x 4 20 The largest doll is 12 inches and the other 3 are the

8 4 4 4 y y 7

height of the next larger doll Use as a factor 3 times

Because 4 is used as a factor 3 times the exponent is 3 So an expression for the height of the smallest doll is

Because y is used as a factor 2 times the exponent is 2 7 7 7 7

So 4 4 4 y y 4 y

3 2 10 10 10 10

9 6 4 6 4 6 4 6 4 b b b 12 12 4 116

Because 6 4 is used as a factor 4 times the exponent is 4

Because b is used as a factor 3 times the exponent is 3 The height of the smallest doll is 4 116 inches

So 6 4 6 4 6 4 6 4 b b b 6 4 b3

21 5 3 23 5 3 8 5 24 29

10 t t t t t

2 7 9 2 63 65

Because t is used as a factor 5 times the exponent is 5

So t t t t t t

23 132 12 2 5 169 144 5 25 5 5

11 52 5 5 25

4 6 32 12 64 6 9

12 11 11 11 11 1331

1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 5

2 2 2 2 2 2 2 64

7 53 12 7 125 12 132 66 66

12 12 12 144

1 1 1 1 1 16

1 1 1 1 1 2 4 8 16 8 1

9 9 9 9 729

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Chapter 10

27 h 1 2 Section 10 2

10 2 Activity pp 416 417

2h 1 21 1 1 22 1 3

2h 1 21 1 20 1 2 2 1 21 2 Product

Multiplication Form

h 3 4 22 24 2 2 2 2 2 2 26

2h 1 23 1 7 24 1 15 3 3 3

2h 1 2 3 1 2 2 4 2 2 8 3

73 7 2 7 7 7 7 7 75

h 5 5 1 5 1 5 1 5 1

5 11 5 16 5 17

5 1 5 1 5 1

2h 1 25 1 24 16

You should choose getting paid 2 h 1 dollars because 10 10 10 10

103 105 108

when you work more than 1 hour you will get paid more 10 10 10 10

than the other option

28 a C 100 0 99988 100 0 99988

t 4 5 5 10

99 95 1 1 2 2 2 2 2 1

After 4 years the amount of carbon 14 remaining is 2 2 2

about 99 95 grams

amount remaining b To find the product of two powers with the same base

b percent remaining

original amount add their exponents

99 95 am an am n

c 2 2 24 22 4 26

After 4 years 99 95 of the carbon 14 remains

29 a To travel from A 440 to A it takes 12 notes 73 7 2 73 2 75

b F 440 1 0595

440 1 0595

880 5 11 5 16 5 11 6 5 17

The frequency of A is about 880 vibrations per

103 105 103 5 108

c Sample answer For a 12 note increase the frequency

5 5 5 5 10

approximately doubles 1 1 1 1

Fair Game Review

Using the rule to simplify the products results in the

30 The statement 8 x x 8 represents the

values in the third column of the table in part a

Commutative Property of Multiplication

31 The statement 2 10 x 2 10 x represents the

Associative Property of Multiplication

32 The statement 3 x 1 3 x represents the Identity

5 17 89 741 1

Property of Multiplication

18 27 108 100 000 000

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Chapter 10

32 10 2 On Your Own p 419

2 a 3 3 3 3 3 3 36

1 62 64 62 4 66

22 2 2 2 2 2 2 2 2 28

c 7 7 7 7 7 7 7 6

d y y y y y y y y y y 9

3 z z12 z1 12 z13

e x x x x x x x x x8

4 44 3 412

General Rule a m a m n

5 y 2 4 y8

2 3 2 3 2 3 2 3 2 3

2 5 2 5 2 5 2 2 6 4 3 2

5 4 5 4 5 4 5 4 53 43

7 54 y 4 625 y 4

6a 6a 6a 6a 6a 64 a 4

3 x 3 x 3 x 3 x

9 0 52 m 2 n 2 0 25m 2 n 2

General Rule a b

Total number Number of bytes Number of

4 a For 3 5 2 x 2 y 23 25 8 32 256 10

of bytes in a gigabyte gigabytes

There are 256 pennies in the stack 230 16

b 2 x 2 y 32 230 24

2 x y 32 230 4

The stacks that have 32 pennies are the locations in The computer has 234 bytes of free storage space

which the sum x y equals 5

10 2 Exercises pp 420 421

Vocabulary and Concept Check

1 4 5 1 Use the Product of Powers Property to multiply powers

2 3 5 with the same base

3 2 5 2 no The bases are not the same

4 1 5 Practice and Problem Solving

3 32 32 32 2 34

The locations 1 4 2 3 3 2 and 4 1 have

32 pennies in their stacks 4 810 84 810 4 814

c The tallest stack is located at 8 8

5 7 5 7 12

2 2 2 2 256 256 65 536

The value of a penny is 0 01 So there is 6 a 3 a 3 a 3 3 a 6

0 01 65 536 655 36 in the tallest stack

7 h 6 h h 6 1 h 7

d From part c the tallest stack has 65 536 pennies

So the height of the tallest stack is 2 6 2 6 8

65 536 0 06 3932 16 inches 2 2 2 2

5 If the same pattern holds true for every example you

encounter then you can use inductive reasoning to write

a general rule stating that the pattern is always true

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Chapter 10

8 9 8 9 17 4 4

5 5 5 5 1 1 1

9 26 16 x 16 x 4 16 x 4 x 4

7 7 7 7 2 2 16

10 2 9 2 9

27 52 53 52 52 53 2

11 54 3 512

12 b12 3 b36

13 3 83 4 3 812 28 highest altitude 3 lowest altitude

The highest altitude of an altocumulus cloud is about

15 The bases should not be multiplied

52 59 52 9 511

16 You should multiply the exponents instead of adding 29 a V p abc

r 6 4 r 24 4

17 63 g 3 216 g 3

3v 3 v5 243v5

2 2 The volume of the egg is 16p 50 27 cubic inches

5 5 25 b a 2 22

1 24 m 4 2 0736m 4

21 r12t12 V p abc

p 22 22 32

22 p p3 p3 3

23 No They are not equal

32 33 35 243 but 32 33 9 27 36 p 24 9

24 a V s 3 3w

An expression for the volume of the case is 3w

b 33 w3 27 w3

The volume of the egg is 192p 603 19 cubic inches

Because 16p 12 192p the volume is 12 times

25 2 4 25 22 24 5 2 2 2 greater than the volume in part a

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Chapter 10

30 Because the side lengths of the base increase by 50 or Section 10 3

0 5 the lengths increase by a factor of 150 of 1 or 1 5

10 3 Activity pp 422 423

1 Quotient Repeated Multiplication Form Power

1 24 2 2 2 2

1 52 b 2 h

2 25 b 2 h

0 75b 2 h or b 2 h

Total pieces

Amount delivered Number of

of mail each second seconds 1 1

7 7 7 7 74

3 5 4 2 2 73

216 34 54 1 1 1

The United States Postal Service delivers 2 16

4 4 1 1 1 1 1

pieces of mail in 6 days 8 5 8 5 8 5 8 5 8 5

32 a 25 2 x 256 8 59 8 5 8 5 8 5 8 5

5 x 8 8 56 8 5 8 5 8 5 8 5

25 x 28 8 5 8 5

Because 5 3 8 x 3 1 1

2 x 1 1 1 1 1

b 10 10 10 10 10

3 3 729 10 8

10 10 10 103

10 10 10 10 10

3 3 3 1 1 1 1 1

3 3 3 3 3 3 3 3

Because 2 4 6 x 4 3 3 3 3 3 3 38

Fair Game Review 1 1 1 1

4 4 4 5 5 5 25 1 1 1 1 1

33 4 34 25

4 1 5 1 5 5 5 5 5

2 3 3 8 6 6 6 5 5 5 5 5

35 3 36 6 1 1 1 1 1

n 2 180 8 2 180 114 11 11 11 11

n 8 111 11

Each angle measures 135

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Chapter 10

b To find the quotient of two powers with the same 10 3 On Your Own pp 424 425

base subtract their exponents

am 1 9 7 4 93

c 24 2 22 2 4 26 5 4 21 4 2

8 59 6 8 53

8 56 215 215 215

8 5 3 5 8 215 8 27

312 6 8 d 5 1 d 9 8 d 4 d 1 d 4 1 d 5

312 4 38 d d

2 7 59 4 55 2 55 53 58

People per Population in 2030

114 1 113 square kilometer Land area

Using the rule to simplify the quotients results in the

values in the third column of the table in part a 217

2 Larger 2

Volume Volume

Volume 2 25 221 17

of Smaller of Larger Answer

Cube Cube Smaller 2 25 24

There will be about 36 people per square kilometer in

Alabama in 2030

b 33 36 33

33 10 3 Exercises pp 426 427

62 Vocabulary and Concept Check

c 63 66 63

63 1 To divide powers means to divide out the common

106 factors of the numerator and denominator To divide

103 powers with the same base subtract their exponents

The volume of the smaller cube equals the number of 2 The third quotient does not belong because it is a quotient

smaller cubes that will fit inside the larger cube of powers with different bases whereas the other three

are quotients of powers with the same bases

3 To divide two powers that have the same base subtract

their exponents Practice and Problem Solving

Sample answer 25 3 22 3 610 4 66 4 89 7 82

7 9 1 7 8 3

71 5 6 4 55 3 4 52

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Chapter 10

644 63 w 63

8 644 3 641 64 24 2 w 63 2 w 61 w 6 w

5 a 3 b 4 54 b 4 54

a 3 b 4 2 5 4 1

10 a 3 b 2 53

7 9 125a 3b 2

512 c10 d 2 512 c10

11 59 c9 59 c

512 9 c10 9 d 2

12 p 11 7 p 4 13 b 24 11 b13

p7 b11 125cd 2

n18 x15 y 9 x15 y9

14 n18 7 n11 27 8 3

8 3 x15 8 y 9 3 x 7 y 6

n7 x y x y

15 When dividing powers you subtract exponents instead of m10 n 7 m10 n 7

28 1 6 m10 1 n 7 6 m9 n1 m9 n

dividing them mn1 6

615 5 610 24

65 29 a 24 2 22 4

75 73 75 3 78 MP3 Player D has 22 4 times more memory than

2 2 78 2 7 6

7 7 7 MP3 Player B

219 25 219 5 2 24 270

17 12 3 15 224 15 29 240

Price dollars

1 1 0 4 8 12 16 20 24 28 32 36 x

M emory GB

no The graph is not a line so memory and price do

not show a linear relationship

19 18 4 22 p 30 22 p 8

p 18 p 4 p p 30 a Sample answer To satisfy the equation the difference

m n must equal 2 When m 4 and n 2 the

c 22 c 22 c 22 difference m n 4 2 is 2

20 8 8 9 17 c 22 17 c 5

b infinitely many solutions Any two numbers that

13 17 satisfy the equation m n 2 are solutions

21 11 k 13 5 k 17 11 k 8 k 6 k 8 6 k 14

22 1014 6 108

The sound of a jet at takeoff is 108 times more intense

than the sound of a normal conversation

x 5 x 48 5 x 43 64 x

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Chapter 10

Number of Number of stars in the Universe Section 10 4

galaxies Number of stars in the Milky Way Galaxy 10 4 Activity pp 428 429

10 1010 Quotient of

Quotient Power

24 Powers Property

24 53 3 50

1024 11 62 2 60

There are about 1013 galaxies in the Universe

83 x 2 x 1 89

83 x 2 x 1 89 53 125 62 36

8 x 1 89 5 125 6 36 81

For the equation to be true the value of x 1 must 4

equal 9 1 They are all equal to 1

c Because all the expressions in part b simplify to 1

1 1 you can equate the powers in the last column of the

x 10 table in part a to 1 So based on these results you

So x 10 can conclude that a 0 1 where a 0

Fair Game Review 2 a

Product of

33 4 5 4 5 9 Product Power

Powers Property

34 23 15 23 15 8 30 3 4 30 4 34

35 33 28 33 28 61 82 80 82 0 82

36 18 22 18 22 4 2 2 2 2

37 B 2 x x 90 1 1 1 1

3 x 90 3 3 3 3

x 30 b yes Each product is equal to the value of the number

with the nonzero exponent This implies that the

numbers with the zero exponents are equal to 1 So

based on these results you can conclude that a 0 1

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Chapter 10

3 a 45 4 3 45 3 42

Product of 6 4 2 2 40 1

Product Power 42 42 42

Powers Property

5 3 53 5 3 3 50 7 8x 2

62 6 2 62 2 60 1 1

8 b 0 b 10 1 10

9 z6 9 z 3

15 z 9 15 15 15 z 3

b They are all equal to 1 1

10 3600 5 5 3600

c From the Multiplicative Inverse Property you know

that the product of a number and its reciprocal is 1 1

d Because each product is equal 1 you can conclude

that the numbers in the product are reciprocals So 3600

a n is equal to the reciprocal of a n or n

4 a The exponents decrease by 1 1 152

ones 10 So 1 152 liters of water leak from the faucet in 1 hour

tenths 10 10 4 Exercises pp 432 433

hundredths 10 2 Vocabulary and Concept Check

thousandths 10 3 1 no For any nonzero number a the value of a 0 1

b 3452 867

3 103 4 102 5 101 2 100 2 Rewrite 10 3 as or

8 10 1 6 10 2 7 10 3

3 1000 4 100 5 10 2 1 3 The numbers in order from least to greatest are 5 5 50

1 1 1 and 54

10 100 1000

3000 400 50 2 0 8 0 06 0 007 4 The last statement does not belong

5 Any nonzero number with an exponent of 0 is equal to 1

Any nonzero number with a negative integer exponent 1 1 1

can be written as the reciprocal of the nonzero number 3 3 3

with its positive integer exponent

Practice and Problem Solving

10 4 On Your Own pp 430 431

1 1 1 1 5 87 7 80 1

6 50 53 50 3 53 125

3 3 8 94 9 4 9 90 1

1 1 1 1 1 1 1 1 1

5 4 7 7 4 3 9 6 2 10 1580 1

5 5 125 62 36

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Chapter 10

43 1 1 8 x3 8 4

11 4 3 5 4 2 2 24 x 3 9 4 x 6 6

45 4 16 2 x9 2 x

3 1 1 25 3d 4 4d 4 3 4 d 4 d 4

3 12 d 4 4

13 4 2 4 5 4 5 12 1

1 26 m 2 n 3 n3 2

1 3 2 k 0 w0 3 2 1 1 w6 w6

1 1 28 Sample answer

14 3 3 3 2 3 3 2 3 5

1 1 1 1 1 1 1 2 16 4 16

15 3 3 6 3

5 3 5 6 5 56 5 5 125

decimeter 10 1 m

29 10 1 3 10 2 100

millimeter 10 3 m

16 There are 100 millimeters in a decimeter

1 5 2 1 5 4 2 4

1 5 2 centimeter 10 2 m

30 10 2 6 10 4 10 000

micrometer 10 6 m

1 5 There are 10 000 micrometers in a centimeter

millimeter 10 3 m

31 10 3 9 10 6 1 000 000

1 nanometer 10 9 m

17 The negative sign goes with the exponent not the base There are 1 000 000 nanometers in a millimeter

43 64 micrometer 10 m

1000 grams 1 gram of sand 100

18 10 kilograms 10 6

1 kilogram 10 3 gram

104 103 1 000 000

10 7 There are 1 000 000 micrometers in a meter

There are about 107 or 10 000 000 grains of sand 1 10 1

33 a 10 micrometer

10 000 10 000 1000

19 For any nonzero number a a 0 1 So 20 1 and

100 1 10 6

1000 1000 106

20 6 y 4 21 8 2 a 7 1000 1 000 000

5b 2 1 000 000 000

22 9 c 3 4 9 c 7 23 5b 2 3 5b

c 4 b 3 0 000000001 or 10 9

The length of the virus is 10 9 meter

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Chapter 10

b 1 nanometer 10 9 meter Study Help

1 Available at BigIdeasMath com

Quiz 10 1 10 4

meter 1 5 5 5 5

1 000 000 000

0 000000001 meter Because 5 is used as a factor 4 times the exponent is 4

The answer to part a is equal to one nanometer So 5 5 5 5 5

34 a 500 103 mm 3 2 7 7 m m m

Because 7 is used as a factor 2 times the exponent is 2

The donation is 500 103 cubic millimeters Because m is used as a factor 3 times the exponent is 3

500 103 104 500 103 4 So 7 7 m m m 7 2 m3

500 10 000 000 3 54 5 5 5 5 625

5 000 000 000

2 2 2 2 2 2 2 64

There are about five billion white blood cells in the

4 8 4 8 4 8 4 8 1

b 500 10 5 10

500 5 10 103 6

2500 103 6 54 1 1

6 5 4 7 5 3 3

2500 109 57 5 125

2500 1 000 000 000

7 38 3 38 1 39

2 500 000 000 000

There are about two trillion five hundred billion red 8 a5 3 a15

blood cells in the donation

c The ratio of red blood cells to white blood cells is 3c

9 34 c 4 81c 4

2 500 000 000 000 500

There are about 500

5 000 000 000 1 2 2

times more red blood cells than white blood cells 10 p p2 p

35 Sample answer Write the power as 1 divided by the

power and use a negative exponent a n a n

1 11 87 4 83

1 63 6 7 63 7 610

36 If you substitute 0 for a you get Zero raised to any 12 2 610 2 68

nonzero exponent is 0 Because division by 0 is

undefined the rule for negative exponents does not p 15 p 15 p 15

apply when a 0 13 3 9 12 p 15 12 p 3

Fair Game Review t13 t 8

14 6 t13 5 t 8 6 t 8 t 2 t 8 2 t10

37 103 106 103 6 109 t5 t

38 102 10 102 1 103 8

39 108 4 10 4 12 x 5 3

10 4 16 3 x 5 7 3 x 2 2

40 D A stem and leaf plot orders numerical data and shows

how they are distributed

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Chapter 10

1000 103 4 A 2 100 2

17 a 1000 10 6 6

103 6 10 3

10 106 The unit that is most appropriate for a door height of 2

The length of the dinoflagellate is 10 3 meter is meters

1000 mm 1m B 1 6 104 16 000

1000 1000 The unit that is most appropriate for a volcano height

1 of 16 000 is feet

1 mm m 0 001 m

1000 C 1 4 102 140

So the length of the dinoflagellate is 1 millimeter The unit that is most appropriate for a pen length of

140 is millimeters

18 107 2 105 D 6 3 10 1 0 63

The unit that is most appropriate for a steel ball

An earthquake of magnitude 8 0 is 105 times stronger

bearing diameter of 0 63 is centimeters

than an earthquake of magnitude 3 0

E 7 5 101 75

Section 10 5 The unit that is most appropriate for a beach ball

10 5 Activity pp 436 437 circumference of 75 is inches

1 2 000 000 000 5 Numbers that are written in scientific notation are

3 000 000 000

represented by the product of a factor that is at least 1 and

6 000 000 000 000 000 000

less than 10 and a power of 10 This type of notation is

6 0 is a factor of 6 000 000 000 000 000 000 and E 18 called scientific notation because it is used in scientific

represents how many places the decimal point is from fields of study Scientific notation is important because

the number in standard form you can use the notation to easily write very large or very

small numbers

The calculator did not show the answer in standard form

because the calculator screen is not large enough to 10 5 On Your Own p 439

display the number

1 The factor is greater than 10 So the number 12 104

2 0 000000002 is not written in scientific notation

0 000000003

0 000000000000000006 2 6 107 60 000 000

6 0 is a factor of 0 000000000000000006 and E 18 7

represents how many places the decimal point is from

The number in standard form is 60 000 000

the number in standard form

3 A This picture appears to have been taken about 3 9 9 10 5 0 000099

1 centimeter or 0 01 meter away from the frog 5

so this picture matches with 10 2 meter The number in standard form is 0 000099

B This picture appears to have been taken about

100 meters away from the frog so this picture 4 1 285 10 4 12 850

matches with 102 meters 4

C This picture appears to have been taken very far away The number in standard form is 12 850

from the frog about 100 000 meters So this picture

matches with 105 meters 5 Water 1 0 103 1000

D This picture appears to have been taken about Lead 1 14 104 11 400

10 centimeters or 0 1 meter away from the frog

Lead is denser than water so it will sink

so this picture matches with 10 1 meter

E This picture appears to have been taken very close to 6 1 4 10 5 75 0 000014 75 0 00105

the frog about 0 00001 meter away So this picture

The fleas consume about 0 00105 liter or 1 05 milliliters

matches with 10 5 meter of blood per day

F This picture appears to have been taken about 1 meter

away from the frog So this picture matches with

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Chapter 10

10 5 Exercises pp 440 441 16 8 10 3 0 008

Vocabulary and Concept Check 3

1 Scientific notation uses a factor of greater than or equal The number in standard form is 0 008

to one but less than 10 multiplied by a power of 10

A number in standard form is written out with all the 17 5 102 500

zeros and place values included 2

2 The expression 10 9 2 13 does not belong because it is The number in standard form is 500

not written in scientific notation the factor is not less

than 10 and the power is not a power of 10 whereas the 18 2 7 10 4 0 00027

other three expressions are written in scientific notation 4

Practice and Problem Solving The number in standard form is 0 00027

3 5 600 000 000 000

19 4 4 10 5 0 000044

4 0 00000000021 5

5 87 300 000 000 000 000

The number in standard form is 0 000044

6 The factor is greater than or equal to 1 and less than 10 20 2 1 103 2100

The power of 10 has an integer exponent So the number 3

1 8 109 is written in scientific notation The number in standard form is 2100

7 The factor is greater than or equal to 1 and less than 10

21 1 66 109 1 660 000 000

The power of 10 has an integer exponent So the number

3 45 1014 is written in scientific notation 9

The number in standard form is 1 660 000 000

8 The factor is less than 1 So the number 0 26 10 25 is

not written in scientific notation 22 3 85 10 8 0 0000000385

9 The factor is greater than 10 So the number 10 5 1012

is not written in scientific notation The number in standard form is 0 0000000385

23 9 725 106 9 725 000

10 The factor is greater than 10 So the number 46 10 17

is not written in scientific notation 6

The number in standard form is 9 725 000

11 The factor is greater than or equal to 1 and less than 10

The power of 10 has an integer exponent So the number 24 Because the exponent is negative the decimal point

5 10 19 is written in scientific notation should be moved to the left not to the right

12 The factor is greater than or equal to 1 and less than 10 4 1 10 6 0 0000041

The power of 10 has an integer exponent So the number 6

7 814 10 36 is written in scientific notation The number in standard form is 0 0000041

13 The factor is less than 1 So the number 0 999 1042 is 25 a 2 7 108 3 270 000 000 3 810 000 000

not written in scientific notation There are 810 000 000 platelets in 3 milliliters of

14 The factor is greater than or equal to 1 and less than 10

The power of 10 has an integer exponent So the number b 5 L 5000 mL

6 022 1023 is written in scientific notation

2 7 108 5000 270 000 000 5000

15 7 107 70 000 000 1 350 000 000 000

7 There are about 1 350 000 000 000 platelets in an

adult body

The number in standard form is 70 000 000

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