Sample problemThe following problem shows how when a negative exponent is applied you divide instead of multiplying as you would when a positive exponent is present.
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Definitions:
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Sample problemIn the sample problem above it is shown on how in scientific notation you may move the decimal as many times as the exponent tells you to. For example , in this problem in order to solve it you move the decimal 9 times due to the exponent being 9 , if it was a negative exponent you would have to move the decimal to the left 9 times.
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EXPLANATION:
When dealing with scientific notation if the exponent is positive you may move the decimal to the right in order to make the number larger , if the exponent is negative than the decimal will move to the left in order to make the number smaller. also the exponent will tell you how many spaces you need to move the decimal. For example if the exponent was a -3 then you would move your decimal to the left 3 times. When dealing with negative exponents you do NOT multiply as you would for when you get a positive exponent. Instead you will do the complete opposite and divide when a negative exponent is present. For example if the problem says 3 to the power of negative 4 , you will end up with a solution of 1/3 to the fourth power. due to the exponent being negative you will put 1 over 3 to get the negative exponent to turn into a positive exponent. |
Similarities: Both scientific notation and negative exponents have to do with exponents and distributing it efficiently and correctly.
Differences: When dealing with negative exponents you only divide and when you are dealing with scientific notation you can either multiply or divide depending on the exponent. |
A scientific notation Real-World example would be a pool decreasing with water due to the decreasing rate of the water in the pool.
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An increase in ones salary is a Real-World example of scientific notation due to the increasing rate in the salary amount.
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Negative exponents in Real-World can be shown in the article/picture above.
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Sources:
Definitions: https://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html
http://www.mathsisfun.com/algebra/negative-exponents.html
Sample problems: https://quizlet.com/79374228/scientific-notation-flash-cards/
http://www.coolmath.com/prealgebra/04-exponents/04-exponents-negative-01
Real Life examples: http://passyworldofmathematics.com/exponents-in-the-real-world/
https://www.1066pools.co.uk/pool_liners_sussex_kent.html
https://lh3.googleusercontent.com/LlzwwnaPVSslEQU0r0YqdJO0DydK5rgf8xDqNJqktP995TEBZuusoY3bQ4NqDmh3nXUSmzI=s118
Definitions: https://www.chem.tamu.edu/class/fyp/mathrev/mr-scnot.html
http://www.mathsisfun.com/algebra/negative-exponents.html
Sample problems: https://quizlet.com/79374228/scientific-notation-flash-cards/
http://www.coolmath.com/prealgebra/04-exponents/04-exponents-negative-01
Real Life examples: http://passyworldofmathematics.com/exponents-in-the-real-world/
https://www.1066pools.co.uk/pool_liners_sussex_kent.html
https://lh3.googleusercontent.com/LlzwwnaPVSslEQU0r0YqdJO0DydK5rgf8xDqNJqktP995TEBZuusoY3bQ4NqDmh3nXUSmzI=s118