2.01 Basic Math. Dr. Fred Garces. Scientific (Exponential) Notation. Chemistry 152. Miramar College Basic Math
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1 2.01 Basic Math Scientific (Exponential) Notation Dr. Fred Garces Chemistry 152 Miramar College Basic Math
2 Environmental Problems in our Lifetime The sun and our atmosphere Basic Math
3 Relationship between CO 2 and Global Temperature Atmospheric CO2 and Global Temperature Basic Math
4 Charles David Keeling, An Analytical Chemist Charles David Keeling Global temp increase 0.6 in last century Basic Math
5 Science and the use of large numbers In science we deal with either very large numbers. - For example: How many Copper atoms are in a single penny? atoms of copper. That s 295 followed by 20 zeros!!! or = atoms of copper Basic Math
6 Science also use very small numbers... or we deal with very small numbers. For example: What is the mass (lb.) of a single copper atom? lb. of copper. That s 24 zeros in front of 23!!! or = lb. of copper Basic Math
7 Why use exponential notation? The exponential notation system makes it easier to manipulate very large numbers in numerical calculations. Example : =??? Numbers with lots of zeros cannot be accommodated by simple calculators unless exponential notation is used Basic Math
8 Writing in Scientific Notation Some sizes of common items. 1. 7, 901 miles 2. 4,800 ft lb 4..07oz (or 2 grams) Basic Math
9 Convenience of Exponential numbers A very large numbers consist of extraneous zeros. These zeros are simply decimal place holder. These zeros can be express by exponents. For example in the 1000 can be express in exponential notation by the following process can be express as 10 x 10 x 10 or 10 multiplied by itself 3 times or Where 3 is the exponent or the power which indicates how many times 10 is multiplied by itself = 10 x 10 x 10 = Basic Math
10 Exponential Notation is based on powers of 10. The exponential notation system is based on powers of 10s and the number of times 10 (ten) is multiplied by itself. Example of scientific notation: For some numbers equal to or greater than one. 1 = 1 x (10 x 0 ) = Where 10 is multiplied by itself 0 times. 10 = 1 x 10 = Where 10 is multiplied by itself one time. 100 = 1 x 10 x 10 = Where 10 is multiplied by itself twice = 1 x 10 x 10 x 10 = Where 10 is multiplied by itself three times. 100,000 = 1 x 10 x 10 x 10 x 10 x 10 = Where 5 is the exponent or the power which indicates how many times 10 is multiplied by itself Basic Math
11 ... powers of 10 For numbers smaller than one i.e., 0.1, or , are based on 1/10 and the number of times it is multiplied by itself. Example of scientific notation: For numbers equal to or less than one. 0.1 = 1 x 1/10 = 1 1/10 1 = Where 1/10 is multiplied by itself one (1) time = 1 x 1/10 x 1/10 = 1 1/10 2 = Where 1/10 is multiplied by itself two (2) times = 1 x 1/10 x 1/10 x 1/10 x 1/10 = 1 1/10 4 = Where 1/10 is multiplied by itself 4 time = 1x 1/10 x 1/10 x 1/10 x 1/10 x 1/10 x 1/10 = 1 1/10 6 = Where 6 is the exponent or the power of the exponent which indicates how many times 1/10 is multiplied by itself Basic Math
12 POWER x 10 Illustrated is dimension of matter in powers of ten. Landmass: m Man: m Cells : m Subatomic : m Milky Way: m Basic Math
13 Exponential Notation involving non-unity numbers Other numbers expressed in exponential notation. For non-unity numbers (numbers that do not begin with 1, i.e., 10, 10,000, ), instead of initially multiplying by one, the exponential notation procedure is started by multiplying by the given number and then multiplying by 10. Exponential notation for some number greater than one , given number is 224 so = 224 x 10 x 10 = 224 x 100 = = = 2.24e = 6.2 x = = 6.2e5 Exponential notation for some number smaller than one = 4.5 x 1/10 x 1/10 = 4.5 1/10 2 = = 4.5e = 6.33 x 1/10 x 1/10 x 1/10 x 1/10 = 6.33 x.0001 = Basic Math
14 SideBar: moving decimal places to change exponent A major source of confusion when learning about exponential notation is how to change the exponent if the decimal point is moved. Example1 : Given What is the new number if the decimal place is moved three places to the right? In our example ? Example2 : Given What is the new number if the decimal place is moved two places to the left? In our example ? Recall the number system: negative numbers are on the left, positive numbers are to the right Working it out Basic Math
15 SideBar: moving decimal places to change exponent A major source of confusion when learning about exponential notation is how to change the exponent if the decimal point is moved. Example1 : Given What is the new number if the decimal place is moved three places to the right? In our example ? Example1 : Given What is the new number if the decimal place is moved two places to the left? In our example ? Recall the number system: negative numbers are on the left, positive numbers are to the right Negative portion. If the decimal point is moved from the left (negative) to the right, then the exponent becomes smaller or negative = Positive portion. If the decimal point is moved from the right (positive) to the left, then the exponent becomes larger = Basic Math
16 SideBar: converting numbers to exponential notation Numbers greater than one. # > 1, positive exponent i.e., If a numbers is greater than 1, the number will have a positive exponent when converted to exponential notation. To converted the number to exponential notation form, move the decimal from the right to the left, the number of places the decimal moves is the number used in the exponent. For example, = = Numbers less than one (non-negative). # < 1, negative exponent i.e., If a number is less than one, the number will have a negative exponent when converted to exponential notation. To convert the number to exponential form, move the decimal from the left (negative region) to the right (positive region). The number of places the decimal is moved is the exponent used. For example, = Basic Math
17 Math operation: Addition-subtraction Example - keep exponent the same in addition and subtraction operation i) = ii) = iii) = iv) = Consider the following example: Three individual who each gave their loose change to the Salvation Army collection pan. The first had two dollar bills a quarter and two pennies. The second gave two quarters and a few pennies. The third donated three dollar bills and five nickels and one penny. What is the total amount that was collected? Basic Math
18 Math operation: Addition and subtraction. (I) Addition or subtraction of numbers expressed in exponential notation: Keep the exponent consistent in all the numbers in other words keep exponent the same in addition and subtraction operation i) =?? Working it out Basic Math
19 Math operation: Addition and subtraction. (I) Addition or subtraction of numbers expressed in exponential notation: Keep the exponent consistent in all the numbers in other words keep exponent the same in addition and subtraction operation i) =?? = Basic Math
20 ...continue: Addition and subtraction Example ii ii) =?? Less precise: Number is rounded off based on this value. See Significant figures rules = or Basic Math
21 ...continue: Addition and subtraction Example iii iii) =?? Less precise: Number is rounded off based on this value = or = Basic Math
22 ...continue: Addition and subtraction Example iv iv) =?? Less precise: Number is rounded off based on this value or = = Basic Math
23 Math operation: Multiplication and division (II) Multiply or division of numbers expressed in exponential notation: multiply or divide the pre-exponent then add or subtract the exponent of the number. i) x = ii) x = iii) = iv) = Basic Math
24 (2) Math operation: Multiply or division Example - After multiplying or dividing main number, exponents are added together (multiplication) or subtracted from each other (division). Example i i) x =?? Working it out Both number has two significant figures. Answer rounded off based on this value. See Significant figures rules Basic Math
25 (2) Math operation: Multiply or division Example - After multiplying or dividing main number, exponents are added together (multiplication) or subtracted from each other (division). Example i i) x =?? has two significant figures. Answer rounded off based on this value. See Significant figures rules = = = Basic Math
26 ...continue: Multiplication and division Example ii ii) x =?? Least number of significant figures. Answer rounded off based on this value. See Significant figures rules , 000 = 100, 000 = Basic Math
27 ...continue: Multiplication and division Example iii iii) =?? has three significant figures. Answer is rounded off to three significant figures. See Significant figures rules = = Basic Math
28 ...continue: Multiplication and division Example iv iv) Both values have three significant figures. Answer is rounded off to three significant figures. See Significant figures rules = Basic Math
29 Math operation : Combinations using addition / subtraction and multiplication / division Carry out addition / subtraction operation first before the multiplication or division operation ( ) = = ( ) ( ) ( ) = Working it out ( ) = = ( ) + ( ) = = Basic Math
30 Math operation : Combinations using addition / subtraction and multiplication / division Carry out addition / subtraction operation first before the multiplication or division operation ( ) = = ( ) 0.12 ( ) = = ( ) + ( ) = = Basic Math
31 Summary Addition or subtraction operation: Keep exponent consistent then add or subtract the pre-exponents. The exponent will remain the same in the final answer. Multiplication or division: Multiply or divide the pre-exponent then: add the exponents (multiplication) subtract the exponents (division) Basic Math
1.04 Basic Math. Dr. Fred Garces. Scientific (Exponential) Notation. Chemistry 100. Miramar College Basic Math
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