Objectives Express numbers in scientific notation Convert from standard form to scientific notation Convert from scientific notation to standard form Add Subtract Multiply and Divide with scientific notation ID: 337842
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Slide1
Scientific NotationSlide2
Objectives
Express numbers in scientific notation.
Convert from standard form to scientific notation.
Convert from scientific notation to standard form.Add, Subtract, Multiply, and Divide with scientific notation.Slide3
Scientific Notation IntroSlide4
Scientific Notation
Consists of two parts
1. mantissa
The full size number that comes before x 102. characteristicThe exponent that comes after x 10 and is superscriptSlide5
Scientific Notation
Example:
3.00
x 10
15
Mantissa
CharacteristicSlide6
Scientific Notation
To convert a normal number to scientific notation, move the decimal either to the left or right until you have a mantissa which is greater than -10 or less than +10Slide7
Scientific Notation
If the absolute value of the number is smaller than 1, the characteristic will be negative
If the absolute value of the number is larger than 1, the characteristic will be positiveSlide8
Scientific Notation
Example:
542
The absolute value of the number is greater than one so the characteristic is positive
542
Moved to the left two spaces
5.42 x 10
2Slide9
Scientific Notation
Example:
-45000000
The absolute value of the number is greater than one so the characteristic is positive
-45000000
Moved to the left seven spaces
-4.5 x 10
7Slide10
Example:
0.0040
The absolute value of the number is less than one so the characteristic is negative
0.0040
Moved to the right three spaces
4.0 x 10
-3Slide11
Example:
-0.209
The absolute value of the number is less than one so the characteristic is negative
-0.209
Moved to the right one space
-2.09 x 10
-1Slide12
Example
:
9.245
The absolute value of the number is between -10 and +10.
9.245
The decimal is not moved. In this case, the characteristic is zero.
9.245 x10
0Slide13
Let’s Practice
Change 47600000 into scientific notation.
= 4.76 x 10
7Slide14
Let’s Practice
Change 0.0890 into scientific notation.
= 8.90 x 10
-2Slide15
Let’s Practice
Change 50000 into scientific notation.
= 5 x 10
4Slide16
Let’s Practice
Change 50000. into scientific notation.
= 5.0000 x 10
4Slide17
Let’s Practice
Change 0.000005454 into scientific notation.
= 5.454 x 10
-6Slide18
Expanding Scientific Notation to Regular notation
If the characteristic is positive, move the decimal to the right.
If the characteristic is negative, move the decimal to the left.Slide19
Expanding Scientific Notation to Regular notation
Example
6.50 x 10
2
The characteristic tells us to move two places to the right.
650.Slide20
Expanding Scientific Notation to Regular notation
Example
6.50 x 10
-2
The characteristic tells us to move two places to the left.
0.0650Slide21
Let’s Practice
Convert 9.7 x 10
-2
into regular notation.
0.097Slide22
Let’s Practice
Convert 9.7 x 10
2
into regular notation.
970Slide23
Let’s Practice
Convert 5.60 x 10
2
into regular notation.
560.Slide24
Let’s Practice
Convert 6.02 x 10
23
into regular notation.
602,000,000,000,000,000,000,000
Isn’t scientific notation great?Slide25
Fixing Incorrect Scientific Notation
Fix the mantissa by moving the decimal
Add the “fixed” characteristic to the original characteristicSlide26
Example
20.4 x 10
6
(incorrect)
Moved over one space to the left (+) to correct the mantissa
2.04 x 10
(6+1)
2.04 x 10
7
(correct)Slide27
Example
200.4 x 10
-6
(incorrect)
Moved over two spaces to the left (+) to correct the mantissa
2.004 x 10
(-6+2)
2.004 x 10
-4
(correct)Slide28
Example
0.00340 x 10
8
(incorrect)
Moved over three spaces to the right (-) to correct the mantissa
3.40 x 10
(8 + -3)
3.40 x 10
5
(correct)Slide29
Example
0.00340 x 10
-8
(incorrect)
Moved over three spaces to the right (-) to correct the mantissa
3.40 x 10
(-8 + -3)
3.40 x 10
-11
(correct)Slide30
Practice
Fix the following incorrect number.
0.000579 x 10
11
5.79 x 10
(-4 + 11)
5.79 x 10
7
(correct)Slide31
Practice
Fix the following incorrect number.
0.040 x 10
-4
4.0 x 10
(-2 + -4)
4.0 x 10
-6
(correct)Slide32
Practice
Fix the following incorrect number.
770.040 x 10
-9
7.70040 x 10
(2 + -9)
7.70040 x 10
-7
(correct)Slide33
Practice
Fix the following incorrect number.
65070.0 x 10
3
6.50700 x 10
(4 + 3)
6.50700 x 10
7
(correct)Slide34
Adding and Subtracting Scientific Notation
The mantissa MUST have the same characteristic.
Then add or subtract the mantissa.
Finally correct the scientific notation if neededSlide35
Multiplying Numbers in Scientific Notation
Multiply the mantissas
ADD the characteristics together
Correct the number if the mantissas are +10 or greater/-10 or less.Slide36
Dividing Numbers in Scientific Notation
Divide the mantissas
Subtract the characteristic of the denominator from the characteristic of the numerator
Correct the number if the mantissas are +10 or greater/-10 or less.