Scientific Notation Copyright Scott Storla 2015. Scientific Notation A number written in scientific...

Scientific Notation

Copyright Scott Storla 2015

Scientific Notation

A number written in scientific notation has two factors. One factor is a real number with absolute value greater than or equal to 1 but less than 10. The other factor has a base of 10 and an integer exponent.


53 10 21.005 10 08 10

The numbers below are not in scientific notation

50.3 10 215 10 7 3 10

Decimal Notation and Scientific Notation

Decimal Notation 300


2Scientific Notation 3 10

4Scientific Notation 5 10

Decimal Notation 0.0005

Rewriting Values with Nonnegative Exponents


Rewriting in scientific notation (positive exponents)


3,000

Write 3,000 in scientific notation.

3,000

3 10 10 10 33 10

Move three decimal places to the left3,000.

.�

33 10


Write in scientific notation.

75,000

81,100,000

12

641 10

21602 10

47.5 10

78.11 10 11.2 10

1 6=4.1 10 10 74.1 10

2 21=6.02 10 10 23=6.02 10


4 10 10 10 10

4Write 4 10 in decimal notation.

4 44 10 40,000

Rewriting scientific notation in decimal notation(Positive exponents)

0 0 0 0

59 10


Write in decimal notation.

41.75 10

105.006 10

9 900,000

1.75 17,500

5.006 50,060,000,000

Rewriting Values with Negative Exponents



Write 0.03 in scientific notation.

0.03

Move two decimal places to the right.

23 10

0.03��

23 10 3

100 2

3

10

Rewriting to scientific notation(Negative exponents)


Write in scientific notation.

0.0000077

0.000153

0.000000000996

70.8 10

434 10

40.01 10

142.1 10

67.7 10

41.53 10 109.96 10

1 78 10 10 88 10

1 43.4 10 10

2 41 10 10 61 10

1 14.21 10 10 04.21 10

33.4 10


1 1 12

10 10 10

3

12

10

3Write 2 10 in decimal notation.

32 10 32.0 10 0.002

Rewriting from scientific notation to decimal notation(Negative exponents)


53.9 10

Write in decimal notation.

= 1.01 36.121 10

53.9 10 0.000039

81.01 10 =0.0000000101

36.121 10 0.006121

Adding and SubtractingWith Scientific Notation



Adding and Subtracting Using Scientific Notation

You can only add and subtract like terms.

Numbers written in scientific notation are like if they have the same power of 10


Simplify using the distributive property

4 45 10 3 10

45 3 10

42 10


Simplify using the distributive property

2 27 10 8 10

27 8 10

215 101 21.5 10 10

31.5 10


Simplify without using the distributive property

4 44 10 5 10

49 10



2 2 23.5 10 0.8 10 1.7 10

21 10



1 1 18 10 4 10 7 10 111 10

1 11.1 10 10

01.1 10



5 56.09 10 7.701 10 513.791 10

1 51.3791 10 10 41.3791 10

Multiplying with Scientific Notation



Multiplying Using Scientific Notation

The commutative property of multiplication

the order of the factors doesn’t effect the product.

The associative property of multiplication

the grouping of the factors doesn’t effect the product.

23 11Simplify 4 10 2 10

Write your answer in scientific notation.


23 114 210 10

8

23 114 10 02 1

23 114 2 10 10 1210


2 73 10 3 10

Simplify write your answer in scientific notation

2 73 3 10 10

99 10



5 65 10 3 10

5 65 3 10 10

1115 10 1 111.5 10 10

121.5 10



2 48 10 4 10

2 48 4 10 10

632 10

1 63.2 10 10

53.2 10



4 612 10 3 10

4 612 3 10 10

236 101 23.6 10 10

13.6 10

Dividing with Scientific Notation



Dividing Using Scientific Notation

3

28 10Simplify Write your answer in scientific notation.4 10

3

204

108

1

2

3

284

1010

3 210 52 10


11

5

3 10

6 10


11

5

3 10

6 10

60.5 10

1 65 10 10

55 10



13

2565 10

5 10

13

25

65 10

5 10

1213 10

1 121.3 10 10

111.3 10



9

144 10

16 10

9

14

4 10

16 10

9 140.25 10

50.25 10

1 52.5 10 10

42.5 10


11

5

3 10

6 10


13

2565 10

5 10

9

144 10

16 10

Mixed Operations



15 11

25

7 10 9 10

2 10


26

25

63 10

2 10

5131.5 10

1 513.15 10 10

503.15 10


7 3

2 2

1.7 10 4 10

2 10 8 10

5 50.85 10 0.5 10

00.425 10

1 04.25 10 10

14.25 10



124 1083 10326 10

124 10240.5 10

128 10



7 22

15 18

1.25 10 3.1 10

7.75 10 5 10

15

3

3.875 10

38.75 10

120.1 10

1 121 10 10

131 10



Simplify using scientific notation.Write your answer in scientific notation.

4,500 200,000

3 54.5 10 2 10

89 10


0.000006 3,000,000

6 66 10 3 10

018 10

1 01.8 10 10

11.8 10



1,800,000

4,000 60,000,0006

3 7

1.8 10

4 10 6 10

6

10

1.8 10

24 10

40.075 10

2 47.5 10 10 67.5 10


Scientific Notation




4,500 200,000

0.000006 3,000,0001,800,000

3,000 6,000,000

10.000252

0.000000042

124,000

3,000,000

Scientific Notation Copyright Scott Storla 2015. Scientific Notation A number written in scientific...

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