Section 3BSection 3BPutting Numbers in Putting Numbers in

PerspectivePerspective

Pages 152-164Pages 152-164

Scientific NotationScientific Notation

Absolutely critical for very large and very small numbers

The federal debt is The federal debt is $8,700,000,000,000. $8,700,000,000,000.

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

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

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Scientific NotationScientific Notation

Scientific 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::

6,700,000,000 6,700,000,000 = 6.7 × 109

= 6.7 E 9 (calculator)

0.000000000000002 0.000000000000002 = 2.0 × 1015

= 2 E -15 (calculator)

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Scientific NotationScientific Notation

106 = 1 million109 = 1 billion

1012 = 1 trillion

The U.S. federal debt is about $8.7 The U.S. federal debt is about $8.7 trillion trillion (8.7(8.7×10×101212))

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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

KEYKEY::

× 10× 10((positive ppositive p) ) moves decimal moves decimal pp places to places to rightright..

× 10× 10((negativenegative pp) ) moves decimal moves decimal pp places to places to leftleft..

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To convert from scientific To convert from scientific notation: to ordinary notation:notation: to ordinary notation:

Move the decimal point as many Move the decimal point as many spaces as you have powers of 10spaces as you have powers of 10 -- --

Move to the Move to the rightright if the power is if the power is positivepositive and move to theand move to the left if the if the power is power is negative..

Fill in any open spaces with zeros.Fill in any open spaces with zeros.

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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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To convert from ordinary to To convert from ordinary to scientific notation:scientific notation:

Move (and count) the decimal point Move (and count) the decimal point until it lies until it lies after the the first non-zero digit. non-zero digit.

The power of 10 = number of movesThe power of 10 = number of moves. .

The power is The power is positive if the decimal if the decimal moved to the moved to the left and and negativenegative if the if the decimal moved to the decimal moved to the rightright..

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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 CalculatorLook for an “EE”“EE” key

1.7842 1.7842 10 1033

1.7842 1.7842 EE EE 3 3 = = 1784.21784.2

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 = = 9.1 E-49.1 E-4

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Multiply or Dividing with scientific Multiply or Dividing with scientific notation:notation:

Examples:(6.2×103)×(3×105) = (6.2×3)×(103×105)

= 18.6= 18.6××1010(3+5) (3+5)

= 1.86= 1.86 ××1010××101088 = 1.86 = 1.86××101099

4.2 102 = 4.2 × 102

8.4 10-5 8.4 10-5

= .5= .5×× 10 102-(-5) 2-(-5) = .5= .5××10107 7

= 5.= 5.××1010(-1) (-1) ×× 10 107 7 = 5.0 = 5.0×× 10 1066

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More Practice:

(3× 104)×(8 × 105) =

= 24×109

= 2.4×10×109

= 2.4×1010

(6.3× 102)×(1.5 × 10) = = 9.45×103

More Practice:

(9× 103)×(5 × 10-7) =

= 45×10-4

= 4.5×10×10-4

= 4.5×10-3

(4.4× 1099)∕(2 × 1011) = = 2.2×1088

Approximations with scientific Approximations with scientific notation:notation:

Example: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

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More Practice:More Practice:

9642 / 319642 / 31

≈≈ 9,000 9,000 / 30/ 30

= (9= (9×10×1033) / (3 × 10)) / (3 × 10)

= 3= 3×10×1022

= 300= 300

check: 9642 / 31 = 311.0322...

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More Practice:More Practice:

7.253 7.253 × × 291291

≈≈ 7 7 ×× 300 300

= 7= 7 ×× (3×10 (3×1022) )

= 21= 21×10×1022

= 2100= 2100

check: 7.253 / 291 = 2110.623

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Homework for Wednesday:Homework for Wednesday:

Pages 164-165Pages 164-165

# 10, 16, 18, 20a-c, 24, 26# 10, 16, 18, 20a-c, 24, 26

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