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Comparing Scientific Notation Numbers

Lets compare numbers in Scientific Notation

Move the sliders and watch how changing the numbers changes our product.

Here we are working with a tool that lets us compare the different parts of scientific notation. We are able to use the sliders to change our coefficient value (a) and our exponent value (b). When moving these we are not only able to see how the Scientific Notation form changes but also how the number changes in standard form.
1) Start by playing around with the sliders to try and changing them to get the following numbers in standard form: 2.7 x 105                                                                            5.5 x 108 9.2 x 10-3                                                                          8.3 x 10-5
2) Now that you have the hang of the sliders set b=7. Move the "a" slider to different points around 1.9, 3.4, and 9.6. How does changing the coefficient (a)  effect our number?
3) Move slider "a" to 4.8. Now play around with slider b, set it to numbers around -4, 1, 2, 6. How does changing the exponent, "b", effect our number?
4) Now lets look at some different numbers, convert these into standard form: 6.0 x 103 6.0 x 104 7.0 x 103 5) Put these three numbers in order from LEAST to GREATEST: 6) Which gives us the greatest number:
  • increasing the coefficient by 1 (Going from 6.0 x 103 to 7.0 x 103) OR
  • increasing the exponent by 1 (Going from 6.0 x 103 to 6.0 x 104)?
Key Question: Therefore when looking at which number in scientific notation is larger or smaller which should we look at first, the coefficient or the exponent?

7) Lets try it! Place the numbers in order from least to greatest on the number line.

8) Let's do some more comparisons! Chance the Rapper has about 6, 792,000 followers on Instagram while Katy Perry has 6.8 x 107 followers on Instagram. Who has more followers? Hint: What do we have to do first to compare the numbers?
Key Question: So when we are comparing numbers that are in different forms, scientific and standard what do we need to do first?
9) Recently there was a Facebook poll that showed how many people were fans of the different NFL teams. About 2, 500,000 fans said the liked the Packers, about 3.27 x 105 were Bills fans, and 1.95 x 106 people said they liked the Giants. According to the poll which team has the most fans, which team has the least?
10) The average diameter of a type of round shaped bacteria is 0.0000037 meter. The spacing between the two of these bacteria is 2.1 x 10-6 meters. Which length is smaller?