Section 3BSection 3BPutting Numbers in Putting Numbers in

PerspectivePerspective

Pages 154-171Pages 154-171

Scientific NotationScientific NotationAbsolutely critical for very large and

very small numbersEx1/155

The federal debt is $9,100,000,000,000. The federal debt is $9,100,000,000,000.

The diameter of a hydrogen nucleus is The diameter of a hydrogen nucleus is 0.0000000000000001 meter.0.0000000000000001 meter.

Your calculators automatically use it!Your calculators automatically use it!

3-B

Scientific NotationScientific NotationScientific Notation is a format in which a

number is expressed as a number number betweenbetween 1 and 10 1 and 10 multiplied by a power of 10.

ExamplesExamples::

9,100,000,000,000 9,100,000,000,000 = 9.1 1012

= 9.1 E 12 (calculator)

0.0000000000000001 0.0000000000000001 = 1.0 1016

= 1 E -16 (calculator)

3-B

Scientific NotationScientific Notation

106 = 1 million = 1,000,000109 = 1 billion = 1,000,000,000

1012 = 1 trillion = 1,000,000,000,000

• The U.S. federal debt is about $9.1 The U.S. federal debt is about $9.1 trillion trillion ($9.1($9.1×10×101212))

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Ordinary vs Scientific NotationOrdinary vs Scientific Notation

An exercise in powers of 10 and moving the An exercise in powers of 10 and moving the decimaldecimal

KEY:KEY:

X 10X 10((positivepositive pp) ) moves decimal p places to moves decimal p places to rightright..

X 10X 10((negativenegative pp) ) moves decimal p places to moves decimal p places to leftleft..

3-B

Conversion from scientific to Conversion from scientific to ordinaryordinary

Examples:Examples:1.7842 103

= 1784.2= 1784.2

2.111 107

= 21,110,000= 21,110,0009.1 10-4

= .00091= .00091

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Conversion from ordinary to Conversion from ordinary to scientificscientific

Example:Example:1330

= 1.330 = 1.330 10 1033

.00000345

= 3.45 = 3.45 10 10-6-6

527 103

= 5.27 = 5.27 10 102 2 10 103 3 = 5.27= 5.27 10 1055

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Using your CalculatorUsing your Calculator

Look for an “EE”“EE” key1.7842 1.7842 10 1033

1.7842 1.7842 EE EE 3 3 == 1784.2 1784.2 2.111 2.111 10 1077

2.111 2.111 EE EE 7 7 = = 2111000021110000

9.1 9.1 10 10-4-4 9.19.1 EEEE -4-4 == 0.00091 0.00091

10001000 = 1.0 x 10 = 1.0 x 1033

1.01.0 EEEE 33notnot (10)(10) EEEE 33

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More PracticeMore Practice

25/16425/164 Convert from scientific to ordinary Convert from scientific to ordinary

27/16427/164 Convert from ordinary to scientific. Convert from ordinary to scientific.

33/16433/164 Total annual energy consumption in Total annual energy consumption in the US is about 100,000,000,000,000,000,000 the US is about 100,000,000,000,000,000,000 joules.joules.

35/16435/164 The hard drive on my computer has a The hard drive on my computer has a capacity of 12.0 gigabytes (recall ‘giga’ = capacity of 12.0 gigabytes (recall ‘giga’ = billion).billion).

37/16437/164 The diameter of a typical bacterium is The diameter of a typical bacterium is about 0.000001 meter.about 0.000001 meter.

Multiply or Dividing with scientific Multiply or Dividing with scientific notation:notation:Examples: 6200 x 300000(6.2 103)× (3 105) = (6.2×3)×(103×105)

= 18.6= 18.6×10×10(3+5) (3+5)

= 1.86= 1.86 ×10 x 10×10 x 1088 = 1.86 x 10 = 1.86 x 1099

420 4.2 102 = 4.2 × 102

.000084 8.4 10-5 8.4 10-5

= .5= .5×10×102-(-5) 2-(-5) = .5×10= .5×107 7

= 5.= 5.×10×10(-1) (-1) x 10x 107 7 = 5.0 x 10 = 5.0 x 1066

More Practice 29/168More Practice 29/168

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Why Scientific Notation: Why Scientific Notation: ApproximationsApproximationsExample:Example:14927 14927 2213 2213

≈≈ 15000 15000 × 2000× 2000= (1.5= (1.5×10×1044)× (2 × 10)× (2 × 1033))= 3= 3×10×1077

= 30,000,000 (30 million)= 30,000,000 (30 million)check: 14927 2213 = 33,033,451

More Practice: Ex2/1558 million residents produce 1.8 lb or .0009 tons of trash each day. Estimate the total amount of trash produced each day. [225 tons?]

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Why Scientific Notation: Calculator Why Scientific Notation: Calculator IssuesIssues

3-B

Total annual energy consumption in the US is Total annual energy consumption in the US is about 100,000,000,000,000,000,000 joules.about 100,000,000,000,000,000,000 joules.

Convert to kilowatt-hours.Convert to kilowatt-hours.

1100,000,000,000,000,000,000

3.6

kilowatt hourjoules

million joules

20

6

1 10

3.6 10kilowatt hours

= .278 x 1014 = 2.78 x 10(-1) x 1014 = 2.78 x 1013

Homework:Homework:

Pages 168Pages 168

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