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Scientists can work with very large and small numbers much more easily if they are written in scientific notation. II. How to Use Scientific Notation A. In scientific notation, a number is written as the product of two numbers: a coefficient and 10 raised to a power. B. For example: The number 4,500 is written in scientific notation as 4.5 x 103. The coefficient is 4.5. The coefficient must be a number greater than or equal to 1 and smaller than 10. The power of 10 or exponent in this example is 3. The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500. C. If a number is greater than 10, the exponent will be positive and is equal to the number of places the decimal must be moved to the left to write the number in scientific notation. D. If a number is less than 10, the exponent will be negative and is equal to the number of places the decimal must be moved to the right to write the number in scientific notation. E. A number will have an exponent of zero if the number is equal to or greater than 1, but less than ten. F. To write a number in scientific notation: 1) Move the decimal to the right of the first non-zero number. 2) Count how many places the decimal had to be moved. 3) If the decimal had to be moved to the right, the exponent is negative. 4) If the decimal had to be moved to the left, the exponent is positive. G. To emphasize again: the exponent counts how many places you move the decimal to the left or right. III. Practice Problems: A. Express the following in scientific notation: 1) .00012 (1.2 x 10-4) 2) 1000 (1 x 103) 3) 0.01 (1 x 10-2) 4) 12 (1.2 x 101) 5) .987 (9.87 x 10-1) 6) 596 (5.96 x 102) 7) .000 000 7 (7.0 x 10-7) 8) 1,000,000 (1.0 x 106) 9) .001257 (1.26 x 10-3) 10) 987,653,000,000 (9.88 x 1011) 11) 8 (8 x 100) B. Express the following as whole numbers or as decimals. 1) 4.9 x 102 (490) 2) 3.75 x 10-2 (.0375) 3) 5.95 x 10-4 (.000595) 4) 9.46 x 103 (9460) 5) 3.87 x 101 (38.7) 6) 7.10 x 100 (7.10) 7) 8.2 x 10-5 (.000082) IV. Using Scientific Notation in Multiplication, Division, Addition and Subtraction A. Rule for Multiplication: 1. When multiplying numbers written in scientific notation, multiply the first factors and add the exponents. 2. Sample problem: Multiply 3.2 x 10-3 by 2.1 x 105 Multiply 3.2 x 2.1 and add the exponents. Answer: 6.7 x 102 B. Rule for Division: 1. Divide the numerator by the denominator and subtract the exponent in the denominator from the exponent in the numerator. 2. Sample Problem: Divide 6.4 x 106 by 1.7 x 102 Divide 6.4 by 1.7 and subtract the exponent. Answer: 3.8 x 104 C. Rule for Addition and Subtraction: 1. To add or subtract numbers written in scientific notation, you must express them with the same power of ten. 2. Sample Problem: Add 5.8 x 103 and 2.16 x 104 Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 5.8 x 103 = .58 x 104 .58 x 104 + 2.16 x 104 = 2.74 x 104 Scientific Notation I. Scientific Notation A. Scientific Notation is used to: B. Examples 1. The mass of one gold atom is .000 000 000 000 000 000 000 327 gram 2. One gram of hydrogen contains 602 000 000 000 000 000 000 000 hydrogen atoms C. Scientists can work with very large and small numbers much more easily if they are written in scientific notation. II. How to Use Scientific Notation A. In scientific notation, a number is written as the product of two numbers: B. For example: The number 4,500 is written in scientific notation as ______________. The coefficient is __________. The coefficient must be a number: The power of 10 or exponent in this example is _____. The exponent indicates how many times the coefficient must be multiplied by 10 to equal the original number of 4,500. C. If a number is greater than 10, the exponent will be _________ and is equal to the number of places the decimal must be moved to the _______ to write the number in scientific notation. D. If a number is less than 10, the exponent will be __________ and is equal to the number of places the decimal must be moved to the ______ to write the number in scientific notation. E. A number will have an exponent of zero if: F. To write a number in scientific notation: 1. 2. 3. 4. G. To emphasize again: the exponent counts how many places you move the decimal to the left or right. III. Practice Problems: A. Express the following in scientific notation: 1) .00012 2) 1000 3) 0.01 4) 12 5) .987 6) 596 7) .000 000 7 8) 1,000,000 9) .001257 10) 987,653,000,000 11) 8 B. Express the following as whole numbers or as decimals. 1) 4.9 x 102 2) 3.75 x 10-2 3) 5.95 x 10-4 4) 9.46 x 103 5) 3.87 x 101 6) 7.10 x 100 7) 8.2 x 10-5 IV. Using Scientific Notation in Multiplication, Division, Addition and Subtraction A. Rule for Multiplication: 1. When multiplying numbers written in scientific notation: 2. Sample problem: Multiply 3.2 x 10-3 by 2.1 x 105 Multiply 3.2 x 2.1 and add the exponents. Answer: B. Rule for Division: 1. 2. Sample Problem: Divide 6.4 x 106 by 1.7 x 102 Divide 6.4 by 1.7 and subtract the exponent. Answer: C. Rule for Addition and Subtraction: 1. To add or subtract numbers written in scientific notation, you must: 2. Sample Problem: Add 5.8 x 103 and 2.16 x 104 Since the two numbers are not expressed as the same power of ten, one of the numbers will have to be rewritten in the same power of ten as the other. 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Scientific Notation8878…o8ozC8B7o8zCoC8zz 2 Ú Ř'3 eo-2 °żŘ'3A. z333 2 °ŇŘ'3 ed52 °6Ř'3Scientific Notation is used z\)ff3)3)\3„e3f3)ff3)\3e\ef3 2 °œŘ'3 eb 2 ƒżŘ'3 eb 2 V żŘ'3 eb2 ) żŘ'3B. z3332 ) ŇŘ'3Examplesz[g˜f)f\ 2 ) ÷Ř'3 eb2 ü ë Ř'31. The m f333pff3˜_2 ü ń8Ř'3ass of one gold atom is .000 000 000 000 000 000 000 32f\\3f33fff3ff(f3f3f˜3)\333fff3fff3fff2fff3fff3ffe3fff3ff 2 ü uŘ'37ef2 ü ŰŘ'3 graml3f=f˜ 2 ü ŻŘ'3 ec 2 Î ëŘ'3 eb2 Ą ë Ř'32. One graf333Žff3f=f22 Ą € Ř'3m of hydrogen contains 602˜3f33f[f=fgff3\ff3f)f\2fff72 Ą WŘ'3 000 000 000 000 000 000 000 n3fff3ffe3fff3fff3fef3fff3fff3 2 Ą KŘ'3hydrogen atomse[f=ffff3f3f˜\ 2 Ą l!Ř'3 eb 2 t żŘ'3 eb2 GżŘ'3C. „333 2 GÜŘ'3 eZ˜2 G6^Ř'3Scientists can work with very large and small numbers much more easily if they are written in z\)ff3)\3[3[ff3„f=\3„)3f3[f=[3)f=ff3gff3\˜f))3fe˜ff=\3˜f\g3˜f=f3ff\))[3)333ff[3f=f3„=)33ff3)f3)2 6Ř'3scientific notation.\\)ff3)2)\3ff2f3)ff3 2 č Ř'3 ea 2 ěHŘ'3 eb-@2 ĎH#Ř'3II. How to Use Scientific Notation88788y7Cz7oo8…o8ozD8C8o8zCoB7zz 2 ϲŘ'3 eo-2 ĽtŘ'3A. z333 2 Ľ‡Ř'3 ed2 ĽëŘ'3In s3f3\—2 Ľ]Ř'3cientific notation, a number is written as the product of two numbers: a coefficient and 10 \)ff2)3)\2ff3f3)ff33f3ef˜ff=3)\3„=)33ff3f\33ff3e=fff\33f333„f3ff˜ff=\333f3\ff33)[)ff23fff3ff3&2 xëŘ'3raised to a power.=f)\ff33f3f3ef„f=3 2 xœ Ř'3 eb 2 KtŘ'3 eb-2 .tŘ'3B. z333 2 .‡Ř'3 ed}2 .ëLŘ'3For example: The number 4,500 is written in scientific notation as 4.5 x 10pf=3f[f˜f)g333pff3ff˜ff=3f3fff3)\2„=)33ff3)f3\\(ff3)3)\3ff3f2(ff3f\3f3f3[3ffű{˙ź@"Arial- 2 ҆Ř'33eJ-2 .ĐŘ'3. 333 2 .iŘ'3 eb 2 tŘ'3 eb_2 Öë8Ř'3The coefficient is 4.5. The coefficient must be a numbepff3\ff33)[(ff33)\3f3f333off3\ff33)[)ef33˜f\33ff3f3ff˜ffI2 Öx)Ř'3r greater than or equal to 1 and smaller =3f=ff3f=33fff3f=3ffff)33f3f3eff3\˜f))f=32 ŠëŘ'3than 10.3fff3ff3 2 Š‚Ř'3 eb 2 |tŘ'3 eb—2 Oë]Ř'3The power of 10 or exponent in this example is 3. The exponent indicates how many times the pff3ff„f=3f33ff3f=3f[fffff33)f33f)\2f[f˜f)f3)\3f333pff3f[fffff33)ff)\f2f\3ff„3˜ff[33)˜f\33ff3|2 "ëKŘ'3coefficient must be multiplied by 10 to equal the original number of 4,500.0\ff33)\)ef32˜f\33ff3˜f)3)f))ff3f[3fe33f3ffff)33fe3f=)f)ff)3fe˜ff=3f33f3fff3 2 "Ř'3 eb 2 őtŘ'3 eb2 ÇtŘ'3C. „333 2 Ç‘Ř'3 eZ82 ÇëŘ'3If a number is greater than 10333f3ff˜ff=3)\3f=ff3f=33eff3ffs2 ÇPEŘ'3, the exponent will be positive and is equal to the number of places 333ff3e[fffff33„)))3ff3ff\)3)[f2fff3)\3ffff(33f33ff3ff˜ff=3f33f)f\f\2…2 šëQŘ'3the decimal must be moved to the left to write the number in scientific notation.!3ff3ff\)˜f)2˜f\33ff3˜g[ff33f33ff3)f3333f3„=)3f33ff3ff˜ff=3)f3\\)ff3)2)\3ff2f3)ff3 2 šÍŘ'3 ea 2 mtŘ'3 eb2 @tŘ'3D. „33 2 @^Ř'3 e›2 @ë`Ř'3If a number is less than 10, the exponent will be negative and is equal to the number of places 333f3ff˜ff=3)\3)f\\23fff2ff333ff3f[fffff33„)))3ff2ffff3)[f3fff3)\3ffff)33e33ff3ff˜ff=3f33f)f\f\22 ëŘ'3the 3ff3€2 NŘ'3decimal must be moved to the right to write the number in scientific notation.ff\)˜f)2˜f\33ff3˜g[ff33f33ff3=)ff333f3„=)3f33ff3ff˜ff=3)f3\\)ff3(3)\3ef3f3)ff3 2 =Ř'3 ea 2 ĺtŘ'3 eb2 ¸tŘ'3E. z333 2 ¸‡Ř'3 edž2 ¸ëbŘ'3A number will have an exponent of zero if the number is equal to or greater than 1, but less than z3ff˜ff=3„*))3ff[f3ff3f[fffff33f33\f=f3)333ff3fe˜ff=3)\3ffff)33f3f=3f=fe3f=33fff3f33ef33)f\\33fff22 ‹ ëŘ'3ten.3ff3 2 ‹ Ř'3 eb 2 ^!tŘ'3 eb2 1"tŘ'3F. p333 2 1"}Ř'3 enI2 1"ë)Ř'3To write a number in scientific notation:pf3„=)3f3f3ff˜ff=3)f3\\(ff3)3)\3ff3f2(ff3 2 1"VŘ'3 eb)2 #ëŘ'31) Move the decimalf=33˜f[f33fg3ff\)˜f)82 #‘ Ř'3 to the right of the first non33f32ff3=)ff33f333ef33)=\33fff 2 #ăŘ'3-e= 2 # Ř'3zero number. [f=f3ff˜ff=333 2 #˝Ř'3 eb\2 Ö#ë6Ř'32) Count how many places the decimal had to be moved.f=33„fff33ff„3˜fg[3f)f\f\33ff3ff\(˜f)3fff33f3ff3˜f[ff3 2 Ö#0Ř'3 ecz2 Š$ëJŘ'33) If the decimal had to be moved to the right, the exponent is negative.f=333333ff3ff[)˜f)3fff33f3ff3˜f[ff33g33ff3=)ff3333ef3f[fffff33)\3ffff3)[f3 2 Š$ąŘ'3 eby2 |%ëIŘ'34) If the decimal had to be moved to the left, the exponent is positive..f=333333ff3ff[)˜f)3fff33f3ff3˜f[ff33g33ff3)f33333ff2f[fffff33)\3ff\)3)[f3 2 |%úŘ'3 eb 2 O& Ř'3 eb 2 "' Ř'3 eb2 ô'tŘ'3G. Ž333 2 ô'›Ř'3 eP—2 ô'ë]Ř'3To emphasize again: the exponent counts how many places you move the decimal to the left or epf3f˜fff\)\f3fff)f3333ef3f[fffff33\fff3\3ff„2˜ff[3f)f\f\3[ff3˜f[f43ff3ff\)˜f)23f33ff3)f333f=22 Ç(ëŘ'3right.=)ff33 2 Ç(ƒŘ'3 eb 2 š)HŘ'3 eb 2 m*HŘ'3 eb 2 @+HŘ'3 eb 2 ,HŘ'3 eb 2 ĺ,HŘ'3 eb 2 ¸-HŘ'3 eb 2 ‹.HŘ'3 eb 2 ^/HŘ'3 eb-33Ř'Ř'33×'×'Ž3Ž3Ö'Ö'33Ő'Ő'Œ3Œ3Ô'Ô'‹3‹3Ó'Ó'Š3Š3Ň'Ň'‰3‰3Ń'Ń'ˆ3ˆ3Đ'Đ' ‡3 ‡3Ď' Ď'  †3 †3Î' Î'  …3 …3Í' Í'  „3 „3Ě' Ě'  ƒ3 ƒ3Ë' Ë' ‚3‚3Ę'Ę'33É'É'€3€3Č'Č'33Ç'Ç'~3~3Ć'Ć'}3}3Ĺ'Ĺ'|3|3Ä'Ä'{3{3Ă'Ă'z3z3Â'Â'y3y3Á'Á'x3x3Ŕ'Ŕ'w3w3ż'ż'v3v3ž'ž'u3u3˝'˝'t3t3ź'ź's3s3ť'ť'r3r3ş'ş'q3q3š'š' p3 p3¸' ¸' !!o3!o3ˇ'!ˇ'!!""n3"n3ś'"ś'""##m3#m3ľ'#ľ'##$$l3$l3´'$´'$$%%k3%k3ł'%ł'%%ţ˙ŐÍ՜.“—+,ůŽ0 hp˜ ¨ °¸ŔČ Đ đäShelby County Schools+ ř¨ Scientific Notation Title  !"ţ˙˙˙$%&'()*+,-./0123456789:;ţ˙˙˙=>?@ABCDEFGHIJKLMNOPQţ˙˙˙STUVWXYţ˙˙˙ý˙˙˙\ţ˙˙˙ţ˙˙˙ţ˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙Root Entry˙˙˙˙˙˙˙˙ ŔF l2™Ę^€1Table˙˙˙˙˙˙˙˙#`0WordDocument˙˙˙˙˙˙˙˙0DSummaryInformation(˙˙˙˙<h+DocumentSummaryInformation8˙˙˙˙˙˙˙˙˙˙˙˙RCompObj˙˙˙˙˙˙˙˙˙˙˙˙q˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙ţ˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙ţ˙ ˙˙˙˙ ŔFMicrosoft Office Word Document MSWordDocWord.Document.8ô9˛q