University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2021
Views:

336

Pages:

2
Author:

StellarSymphony

Negative Exponents Lga r11 to evaluate negative exponents and use them to write numbers in scientific notation and in standard form. When a whole number has a positive exponent, the value of the power is greater than 1. When a whole number has a negative exponent, the value of the power is less than 1. When any number has a zero exponent, the value of the power is equal to 1. Value Power 102 101 100 10-1 Do you see a pattern in the table at right? The negative exponent becomes positive when it is in the denominator of the fraction. 10-2 10- 3 100 10 1 1 or 0.1 101 102 or0.01 1 1 "io3"or0.001 ) + 10 ) +-a- 10 10 ) ) + 10 ) + 10 lfXAM P II. E •dS Evaluating Negative Exponents ·· ·· 1 : I' Evaluate 10-4, 10- 4 = �4 1 Write the fraction with a positive exponent in the denominator. Evaluate the power. 1 O,OOO .0001 Write the decimal form. =-��-=-�·� ,c,--� s �<"" �' In Chapter 1, you learned to write large numbers in scientific notation using powers of ten with positive exponents. In the same way, you can write very small numbers in scientific notation using powers of ten with negative exponents. ·-.- ' IEXAM P II. E :z,& Writing Smail Numbers in Scientific: Notation i��;!a,- - i number that is greater than or 1 and less ��:',t;, Write 0.000065 in scientific notation. Move the decimal point 5 places 0.000065 = O ..QQQQ§,5 to the right. I , L�=�- = 6.5 0.00001 = 6.5 X 10-5 X .. . Write as a product of two factors. Write in exponential form. Since the decimal point was moved 5 places, the exponent is -5. E X AM P L E L:: ;,,b· Writing Small Numbers in Standard Form I Write 3A x 10-6 in standard form. = 0�4 Since the exponent is -6, move the decimal point 6 places to the left. = 0_0000034 ==--=- ='-"' ,� - ,� When comparing numbers in scientific notation, you may need to compare only the powers of ten to see which value is greater. Comparing Numbers Using Scientific Notation EXAMPLE J,4cf.i ,,. Compare. Write <. >, or =. ·-,l 7 ';,��· �� -:::�� 12 G.l x 10- 12 Since 10-B > 10- 12, 3.7 X Compare the powers of ten. 10- > 6.1 x 10- 12. 8 7.3 x 10-5 10-5 Compare the powers of ten. 10- 5 = 10- 5 Since the powers often are equal, compare the decimals. 4.9 < 7 .3 4 is less than 7. 5 Since 4.9 < 7.3, 4.9 x 10- < 7.3 x 10- 5. ::!U,' 4.9 X Find each value. 2. 10- 6 1. 10-B 3. 10- 5 Write each number in scientific notation or standard form. 7. 0.00086 6. 0.00000021 8. 0.0000000066 10. 0.0009 11. 0.0453 18. 2.77 X 10-l 19. 9.06 14. 5.8 X 10- 9 15. 4.5 X Compare. Write<,>, or =. 22. 7.6 X 10-l 7.7 X 10-l 6 24. 2.8 X 102.8 X 10-7 10-5 X 10-2 5. 10- 7 4. 10- 10 9. 0.007 12. 0.0701 13. 0.00003021 20. 7 X 10-lO 21. 8 16. 3.2 X 10-3 17. 1.4 X 10-ll 23. 8.2 X 10-7 8.1 X 25. 5.5 2.2 X X 10-z X 10-B 10-6 10- 5 :J'l} 26. Write Abouil It Explain the effect that a zero exponent has on a power.