SCIENTIFIC NOTATION GUIDED NOTES AND PRACTICE h c a Te y Eas . X Includes a 2 page notes/reference with examples and practice problems, a 2 page student guided notes with practice problems, and a worksheet with 24 practice problems! ??? ? Hu h? ???? SCIENTIFIC NOTATION Regular Notation (RN)- The standard way that we write our numbers. Ex: Two Hundred and Eight Million is written - 280,000,000. Scientific Notation (SN)- A shorthanded way of writing really large or really small numbers. In SN a number is written as the product of two factors. Ex: 280,000,000 can be written in scientific notation as 2.8 π₯ 10! . S eco nd F acto r Is always a power of 10. The power of the exponent tells you how many places to move the decimal point. The sign of the exponent tells you which direction to move it. F irst Fa ctor A number that is between 1 and 10 It may or may not be a decimal. Regular Notation àο Scientific Notation If Decimal is moved left Exponent will be positive Regular Notation 420,000. 735,000,000. .00897 .0000014 If Decimal is moved to Right Exponent will be negative How to Change Scientific Notation Move the decimal after the 4 and before the 2 That is 5 places to the left Multiply 4.2 by 10 to the 5th power Move the decimal after the 7 and before the 3 That is 8 places to the left Multiply 7.35 by 10 to the 8th power Move the decimal after the 8 and before the 9 That is 3 places to the right Multiply 8.97 by 10 to the -3rd power Move the decimal after the 1 and before the 4 That is 6 places to the right Multiply 1.4 by 10 to the -6th power 4.2 π₯ 10! 7.35 π₯ 10! 8.97 π₯ 10!! 1.4 π₯ 10!! Copyright © Shemiah Hale. All Rights Reserved Scientific Notation àο Regular Notation If exponent is Negative Move decimal to the Left Add zeros where needed. If exponent is Positive Move decimal to the Right Add zeros where needed. Scientific Notation How to Change Regular Notation 7.5 × 10! Exponent is positive 5. Move the decimal 5 places to the right Exponent is positive 4. Move the decimal 4 places to the right Exponent is Negative 3. Move the decimal 3 places to the left. Exponent is Negative 5. Move the decimal 5 places to the left. 750,000. 3.8 × 10! 4.2 × 10!! 7.51 × 10!! 38,000. .0042 .0000751 PRACTICE: Change from Regular Notation to Scientific Notation: Change from Scientific Notation to Regular Notation: 1.) 45,000 2.) 9,000,000 3.) 7,450 4.) .0000378 5.) .05 6.) 670,400 7.) 7,070,000,000 8.) .00000089 9.) .18900097 10.) 570,000,000 1.) 9.46 × 10!! 2.) 2.5 × 10! 3.) 1.6 × 10!! 4.) 4 × 10 ! 5.) 7.25 × 10 ! 6.) 3.2456 × 10!! 7.) 6 × 10!! 8.) 9.7 × 10! 9.) 5.06 × 10!! 10.) 8 × 10! ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ Copyright © Shemiah Hale. All Rights Reserved SCIENTIFIC NOTATION Regular Notation (RN)- The ____________ ______ that we write our numbers. Ex: Two Hundred and Eight Million is written - _________________ Scientific Notation (SN)- A ______________ ______ of writing really large or really small numbers. In SN a number is written as the ___________ of _______ _________. Ex: 280,000,000 can be written in scientific notation as ___________________________ S eco nd F acto r Is always a _____________ The power of the exponent tells you ______________ to move the decimal point. The ______ of the exponent tells you which ___________ to move it. F irst Fa ctor A number that is _________ . It may or may not be ___________. Regular Notation àο Scientific Notation If Decimal is moved ______________. Exponent will be ___________________. Regular Notation 420,000. 735,000,000. .00897 .0000014 If Decimal is moved to _____________. Exponent will be ____________________. How to Change Scientific Notation Move the decimal after the 4 and before the 2 That is 5 places to the left Multiply 4.2 by 10 to the 5th power Move the decimal after the 7 and before the 3 That is 8 places to the left Multiply 7.35 by 10 to the 8th power Move the decimal after the 8 and before the 9 That is 3 places to the right Multiply 8.97 by 10 to the -3rd power Move the decimal after the 1 and before the 4 That is 6 places to the right Multiply 1.4 by 10 to the -6th power Copyright © Shemiah Hale. All Rights Reserved Scientific Notation àο Regular Notation If exponent is ____________________ Move decimal to the _____________ Add zeros where needed. If exponent is _______________________ Move decimal to the ________________ Add zeros where needed. Scientific Notation How to Change 7.5 × 10! Exponent is positive 5. Move the decimal 5 places to the right Exponent is positive 4. Move the decimal 4 places to the right Exponent is Negative 3. Move the decimal 3 places to the left. Exponent is Negative 5. Move the decimal 5 places to the left. 3.8 × 10! 4.2 × 10!! 7.51 × 10!! Regular Notation PRACTICE: Change from Regular Notation to Scientific Notation: Change from Scientific Notation to Regular Notation: 1.) 45,000 2.) 9,000,000 3.) 7,450 4.) .0000378 5.) .05 6.) 670,400 7.) 7,070,000,000 8.) .00000089 9.) .18900097 10.) 570,000,000 1.) 9.46 × 10!! 2.) 2.5 × 10! 3.) 1.6 × 10!! 4.) 4 × 10 ! 5.) 7.25 × 10 ! 6.) 3.2456 × 10!! 7.) 6 × 10!! 8.) 9.7 × 10! 9.) 5.06 × 10!! 10.) 8 × 10! ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ ________________ Copyright © Shemiah Hale. All Rights Reserved ANSWER KEY: Change from Regular Notation to Scientific Notation: 1.) 45,000 2.) 9,000,000 3.) 7,450 4.) .0000378 5.) .05 6.) 670,400 7.) 7,070,000,000 8.) .00000089 9.) .18900097 10.) 570,000,000 4.5 π₯ 10! 9 π₯ 10! 7.45 π₯ 10! 3.78 π₯ 10!! 5 π₯ 10!! 6.704 π₯ 10! 7.070 π₯ 10! 8.9 π₯ 10!! 1.8900097 π₯ 10!! 5.7 π₯ 10! Change from Scientific Notation to Regular Notation: 1.) 9.46 × 10!! 2.) 2.5 × 10! 3.) 1.6 × 10!! 4.) 4 × 10 ! 5.) 7.25 × 10 ! 6.) 3.2456 × 10!! 7.) 6 × 10!! 8.) 9.7 × 10! 9.) 5.06 × 10!! 10.) 8 × 10! .00000946 2500 .016 400,000 72,500 .000000032456 .006 97,000,000 .000506 800 Copyright © Shemiah Hale. All Rights Reserved STUDENT NAME: _____________________________ DATE: _________________ SCIENTIFIC NOTATION CONVERT EACH NUMBER IN SCIENTIFIC NOTATION TO REGULAR NOTATION If exponent is Negative Move decimal to the Left Add zeros where needed. If exponent is Positive Move decimal to the Right Add zeros where needed. 1. π. ππ π ππ!π ____________ 7. π. π π ππ!π ____________ 2. π. π π πππ ____________ 8.π. π π ππ π ____________ 3. π. π π ππ!π ____________ 9. π. π π ππ!π ____________ 4. π. ππ π ππ π ____________ 10. π. ππ π ππ π ____________ 5. π π ππ!π ____________ 11. π. π π ππ!π ____________ 6. π π ππ π ____________ 12. π. π π ππ π ____________ CONVERT EACH NUMBER IN REGULAR NOTATION TO SCIENTIFIC NOTATION If Decimal is moved left Exponent will be positive If Decimal is moved to Right Exponent will be negative 1. 0.0024 ____________ 7. 0.0000035 ____________ 2. 5,604 ____________ 8. 45,995 ____________ 3. 693.75 ____________ 9. 754.256 ____________ 4. 0.087 ____________ 10. 0.0088 ____________ 5. 8,550,000 ____________ 11. 1.8907 ____________ 6. 12,000,000 ____________ 12. 25,009 ___________ Answer key SCIENTIFIC NOTATION CONVERT EACH NUMBER IN SCIENTIFIC NOTATION TO REGULAR NOTATION If exponent is Negative Move decimal to the Left Add zeros where needed. If exponent is Positive Move decimal to the Right Add zeros where needed. 1. π. ππ π ππ!π 0.0247 7. π. π π ππ!π 0.000045 2. π. π π πππ 93,000,000 8. π. π π ππ π 550,000 3. π. π π ππ!π 0.000085 9. π. π π ππ!π 0.63 4. π. ππ π ππ π 2,070,000 10. π. ππ π ππ π 19,800 5. π π ππ!π 0.00000007 11. π. π π ππ!π 0.000024 6. π π ππ π 300 12. π. π π ππ π 92,000,000 CONVERT EACH NUMBER IN REGULAR NOTATION TO SCIENTIFIC NOTATION If Decimal is moved left Exponent will be positive If Decimal is moved to Right Exponent will be negative 1. 0.0024 π. π π ππ!π 7. 0.0000035 π. π π ππ!π 2. 5,604 π. πππ π ππ π 8. 45,995 π. ππππ π ππ π 3. 693.75 π. ππππ π ππ π 9. 754.256 π. πππππ π πππ 4. 0.087 π. π π ππ π 10. 0.0088 π. π π ππ!π 5. 8,550,000 π. πππ π ππ!π 11. 18.907 π. π π ππ π 6. 12,000,000 π. π π ππ π 12. 25,009 π. ππππ π ππ π
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