Respuesta :
You can convert from scientific notation to simple notation using the fact that negative powers can be converted to division.
The correct option is given by
Option C. The greatest number is 8. 2 × 10-3. It is 2,000 times greater than the smallest number.
How does negative power work?
Suppose you have got [tex]a^{-b}[/tex]
Then we have
[tex]a^{-b} = \dfrac{1}{a^b}[/tex]
Converting from scientific notation to normal decimal notation
[tex]8.2 \times 10^{-3} = \dfrac{8.2}{10^3} = \dfrac{8.2}{1000} = 0.0082\\\\5.2 \times 10^{-6} = \dfrac{5.2}{10^6} = \dfrac{5.2}{1000000} = 0.0000052\\\\4.1 \times 10^{-6} = \dfrac{4.1}{10^6} = \dfrac{4.1}{1000000} = 0.0000041[/tex]
Thus, we can see that
The greatest number among given numbers is [tex]8.2 \times 10^{-3}[/tex]
The smallest number among the given numbers is [tex]4.1 \times 10^{-6}[/tex]
Dividing greatest number by smallest to see how many times the greatest number is greater than the smallest number
[tex]\dfrac{8.2 \times 10^{-3}}{4.1 \times 10^{-6}} =\dfrac{8.2}{4.1} \times \dfrac{10^{-3}}{10^{-6}} = 2 \times 10^{-3 - (-6)} = 2 \times 10^3 = 2000[/tex]
Remember that when base are same, and there is division, then power gets subtracted, that's why we got [tex]\dfrac{10^{-3}}{10^{-6}} = 10^{-3 - (-6)} = 10^3[/tex]
Thus, we have the greatest number 2000 times bigger than the smallest number among the numbers given.
Thus, the correct option is
Option C. The greatest number is 8. 2 × [tex]10^{-3}[/tex]. It is 2,000 times greater than the smallest number.
Learn more about scientific notations here:
https://brainly.com/question/8626074
