SCIENTIFIC NOTATION GUIDED NOTES AND PRACTICE

1 SCIENTIFIC . NOTATION GUIDED . NOTES AND PRACTICE . ac h Includes a 2 page NOTES /reference Te y with examples and PRACTICE Eas problems, a 2 page student GUIDED NOTES with PRACTICE problems, and a worksheet with 24 PRACTICE problems! ??? . ? Hu ???? h? X. 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 10! . S eco nd F acto r Is always a power of 10. The power of the exponent F irst Fa ctor tells you how many places A number that is to move the decimal point. between 1 and 10 The sign of the exponent It may or may not tells you which direction be a decimal.

2 To move it. Regular NOTATION SCIENTIFIC NOTATION If Decimal is moved left If Decimal is moved to Right Exponent will be positive Exponent will be negative Regular How to Change SCIENTIFIC NOTATION NOTATION Move the decimal after the 4 and before the 2. 420,000. That is 5 places to the left 10! Multiply by 10 to the 5th power Move the decimal after the 7 and before the 3. 735,000,000. That is 8 places to the left 10! Multiply by 10 to the 8th power Move the decimal after the 8 and before the 9..00897 That is 3 places to the right 10!! Multiply by 10 to the -3rd power Move the decimal after the 1 and before the 4..0000014 That is 6 places to the right 10!! Multiply by 10 to the -6th power Copyright Shemiah Hale. All Rights Reserved SCIENTIFIC NOTATION Regular NOTATION If exponent is Negative If exponent is Positive Move decimal to the Left Move decimal to the Right Add zeros where needed.

3 Add zeros where needed. SCIENTIFIC How to Change Regular NOTATION NOTATION Exponent is positive 5. 10! Move the decimal 5 places to the right 750,000. Exponent is positive 4. 10! Move the decimal 4 places to the right 38,000. Exponent is Negative 3. 10!! Move the decimal 3 places to the left..0042. Exponent is Negative 5. 10!! Move the decimal 5 places to the left..0000751. PRACTICE : Change from Regular NOTATION to Change from SCIENTIFIC NOTATION to SCIENTIFIC NOTATION : Regular NOTATION : 1.) 45,000 _____ 1.) 10!! _____ 2.) 9,000,000 _____ 2.) 10! _____ 3.) 7,450 _____ 3.) 10!! _____ 4.) .0000378 _____ 4.) 4 10 ! _____ 5.) .05 _____ 5.) 10 ! _____ 6.) 670,400 _____ 6.) 10!! _____ 7.) 7,070,000,000 _____ 7.) 6 10!! _____ 8.) .00000089 _____ 8.) 10! _____ 9.) .18900097 _____ 9.) 10!! _____ 10.) 570,000,000 _____ 10.) 8 10! _____ Copyright Shemiah Hale.

4 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 F irst Fa ctor tells you _____. A number that is to move the decimal point. _____ . The _____ of the It may or may not exponent tells you which be _____. _____ to move it. Regular NOTATION SCIENTIFIC NOTATION If Decimal is moved _____. If Decimal is moved to _____. Exponent will be _____. Exponent will be _____. Regular How to Change SCIENTIFIC NOTATION NOTATION Move the decimal after the 4 and before the 2. 420,000. That is 5 places to the left Multiply by 10 to the 5th power Move the decimal after the 7 and before the 3.

5 735,000,000. That is 8 places to the left Multiply by 10 to the 8th power Move the decimal after the 8 and before the 9..00897 That is 3 places to the right Multiply by 10 to the -3rd power Move the decimal after the 1 and before the 4..0000014 That is 6 places to the right Multiply by 10 to the -6th power Copyright Shemiah Hale. All Rights Reserved SCIENTIFIC NOTATION Regular NOTATION If exponent is _____ If exponent is _____ Move decimal to the _____ Move decimal to the _____ Add zeros where needed. Add zeros where needed. SCIENTIFIC How to Change Regular NOTATION NOTATION Exponent is positive 5. 10! Move the decimal 5 places to the right Exponent is positive 4. 10! Move the decimal 4 places to the right Exponent is Negative 3. 10!! Move the decimal 3 places to the left. Exponent is Negative 5. 10!! Move the decimal 5 places to the left. PRACTICE : Change from Regular NOTATION to Change from SCIENTIFIC NOTATION to SCIENTIFIC NOTATION : Regular NOTATION : 1.

6 45,000 _____ 1.) 10!! _____ 2.) 9,000,000 _____ 2.) 10! _____ 3.) 7,450 _____ 3.) 10!! _____ 4.) .0000378 _____ 4.) 4 10 ! _____ 5.) .05 _____ 5.) 10 ! _____ 6.) 670,400 _____ 6.) 10!! _____ 7.) 7,070,000,000 _____ 7.) 6 10!! _____ 8.) .00000089 _____ 8.) 10! _____ 9.) .18900097 _____ 9.) 10!! _____ 10.) 570,000,000 _____ 10.) 8 10! _____ Copyright Shemiah Hale. All Rights Reserved ANSWER KEY: Change from Regular NOTATION to Change from SCIENTIFIC NOTATION to SCIENTIFIC NOTATION : Regular NOTATION : 1.) 45,000 10! 1.) 10!! .00000946 2.) 9,000,000 9 10! 2.) 10! 2500 3.) 7,450 10! 3.) 10!! .016 4.) .0000378 10!! 4.) 4 10 ! 400,000 5.) .05 5 10!! 5.) 10 ! 72,500 6.) 670,400 10! 6.) 10!! .000000032456 7.) 7,070,000,000 10! 7.) 6 10!! .006 8.) .00000089 10!! 8.) 10! 97,000,000 9.) .18900097 10!! 9.) 10!! .000506 10.) 570,000,000 10! 10.) 8 10! 800 Copyright Shemiah Hale.

7 All Rights Reserved STUDENT NAME: _____ DATE: _____. SCIENTIFIC NOTATION . CONVERT EACH NUMBER IN. SCIENTIFIC NOTATION TO REGULAR NOTATION . If exponent is Negative If exponent is Positive Move decimal to the Left Move decimal to the Right Add zeros where needed. Add zeros where needed. 1.. ! _____ 7.. ! _____. 2.. _____ 8.. _____. 3.. ! _____ 9.. ! _____. 4.. _____ 10.. _____. 5. ! _____ 11.. ! _____. 6. _____ 12.. _____. CONVERT EACH NUMBER IN. REGULAR NOTATION TO SCIENTIFIC NOTATION . If Decimal is moved left If Decimal is moved to Right Exponent will be positive Exponent will be negative 1. _____ 7. _____. 2. 5,604 _____ 8. 45,995 _____. 3. _____ 9. _____. 4. _____ 10. _____. 5. 8,550,000 _____ 11. _____. 6. 12,000,000 _____ 12. 25,009 _____. Answer key SCIENTIFIC NOTATION . CONVERT EACH NUMBER IN. SCIENTIFIC NOTATION TO REGULAR NOTATION . If exponent is Negative If exponent is Positive Move decimal to the Left Move decimal to the Right Add zeros where needed.

8 Add zeros where needed. 1.. ! 7.. ! 2.. 93,000,000 8.. 550,000. 3.. ! 9.. ! 4.. 2,070,000 10.. 19,800. 5. ! 11.. ! 6. 300 12.. 92,000,000. CONVERT EACH NUMBER IN. REGULAR NOTATION TO SCIENTIFIC NOTATION . If Decimal is moved left If Decimal is moved to Right Exponent will be positive Exponent will be negative 1.. ! 7.. ! . 2. 5,604 . 8. 45,995 .. 3.. 9.. 4.. 10.. ! . 5. 8,550,000 . ! 11.. 6. 12,000,000 . 12. 25,009.