Scientific Notation Powers of

Ten

“Big” Numbers

“Small” Numbers

Scientific notation is used when writing very large numbers

Large Numbers

1 gram of water contains 330,000,000,000,000,000,000,000

molecules of water

3.3 x 1023

Small Numbers Scientific notation can also be used to

write very small numbers

The mass of one gold atom is 0.000 000 000 000 000 000 000 327 grams

3.27 x 10-22

Powers of Ten In scientific notation, a number is written

as the product of two numbers: a coefficient and a 10 raised to a power.

Power of the Exponent

Power of the Exponent

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Positive Exponent

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Check Answer

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Negative Exponent

Calculator

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Express the Following in Scientific Notation

1. 700 m

2. 38,000 m

3. 4,500,000 m

4. 685,000,000,000 m

5. 0.005 4 kg

6. 0.000 006 87 kg

7. 0.000 000 076 kg

8. 0.000 000 000 8 kg

………….7 x 102 m

………….3.8 x 104 m

………….4.5 x 106 m

…..….6.85 x 1011 m

………….5.4 x 10-3 m

……….6.87 x 10-6 m

………….7.6 x 10-8 m

………….8 x 10-10 m

Express the Following as Standard Numbers

1. 3.6 X 104 s

2. 5.4 x 10-4 s

3. 5.06 x 103 s

4. 9.34 x 10-10 s

5. 103 s

6. 8 x 100 s

7. 8.3 x 10-13 s

8. 10-2 s

…………. 360,000 s

………….0.000 54 s

…………. 5060 s

….. 0.000 000 000 934 s

…………. 1,000 s

………. 8 s

….0.000 000 000 000 83 s

…………. 0.01 s

Adding in Scientific Notation

2.70 X 107 + 15.6 x 106 = ?

2.70 X 107 Leave alone because 2.7 is a

value between 1 and 10

1.56 X 107

Move the decimal once to the

left and increase exponent by

value of 1

15.6 X 106

2.70 X 107 + 1.56 x 107 = 4.26 x 107

Subtraction in Scientific Notation

3.2 x10-8 - 4.9 x 10-5 = ?

3.2 x 10-8 Leave alone because it’s the

larger exponent

0.0049 x 10-8 Move the decimal 3 places to

the left

4.9 x 10-5

3.2 x 10-8 - 0.0049 x 10-8 = 3.1951 x 10-8

Add or Subtract the Following:

1. 5 x 10-5 + 2 x 10-5

2. 7 x 108 – 4 x 108

3. 9 x 102 – 7 x 102

4. 4 x 10-12 + 1 x 10-12

5. 1.26 x 104 + 2.5 x 103

6. 7.06 x 10-3 + 1.2 x 10-4

7. 4.39 x 105 – 2.8 x 104

8. 5.36 x 10-1 – 7.40 x 10-2

…………..7 x 10-5

…………..3 x 108

………….. 2 x 102

…………..5 x 10-12

…………..1.51 x 104

……….. 7.18 x 10-3

…………..4.11 x 105

………..4.62 x 10-1

Multiplication in Scientific Notation

3.7 x 107 x 2.5 x 103 = ?

3.7 x 2.5 = 9.25 Multiply the

coefficients

107 + 103 = 1010 Add the exponents

3.7 x 107 - 2.5 x 103 = 9.25 x 1010

Dividing in Scientific Notation

8.9 x 107 ÷ 4.5 x 10-3 = ?

8.9 ÷ 4.5 = 1.98 Divide the

coefficients

107 – 10-3 = 1010 Subtract the

exponents

8.9 x 107 ÷ 4.5 x 10-3 = 1.98 x 1010

Multiply or Divide the Following:

1. 4 x 102 x 1 x 108

2. 2 x 10-4 x 3 x 102

3. 3 x 101 x 3 x 10-2

4. 1 x 103 x 1 x 10-1

5. 6 x 102 ÷ 2 x 101

6. 8 x 104 ÷ 4 x 101

7. 9 x 105 ÷ 3 x 10-1

8. 4 x 10-3 ÷ 2 x 10-2

…………..4 x 1010

…………..6 x 10-2

………….. 9 x 10-1

…………..5 x 102

…………..3 x 101

……….. 2 x 103

…………..3 x 106

………..2 x 10-1