Inside an orbital laboratory, Emek and Luna examined three meteor samples for traces of a valuable element. The scanner measured the concentrations as 0.000064, 0.0000087, and 0.000052 grams per gram for Samples A, B, and C. The sorting system accepted only scientific notation, so Emek rewrote the measurements as 6.4 x 10^-5, 8.7 x 10^-6, and 5.2 x 10^-5. Luna checked the powers of ten and noted that values with 10^-5 were greater than the positive values shown with 10^-6. The collection requirement was a concentration of at least 5.0 x 10^-5 grams per gram. Samples A and C met the requirement, while Sample B did not. To decide which specimen should be studied first, they compared the coefficients of the two qualifying samples. Since 6.4 was greater than 5.2, Sample A had the higher concentration. They placed Samples A and C in the research chamber, with Sample A first in line for detailed analysis.

Challenges

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Challenge 1 of 5

Challenges

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Challenge 1 of 4
Hint
The powers of 10 are the same, so compare the coefficients 4.9 and 5.0.
A new Sample D has a concentration of 4.9 x 10^-5 grams per gram. Which statement correctly compares Sample D with the collection requirement of at least 5.0 x 10^-5 grams per gram?
Sample D qualifies because 4.9 is greater than 5.0.Sample D qualifies because both values use 10^-5.Sample D does not qualify because 4.9 x 10^-5 is less than 5.0 x 10^-5.Sample D does not qualify because 10^-5 is less than 0.
Correct. With equal powers of 10, 4.9 < 5.0, so Sample D does not meet the requirement.
When the powers of 10 match, compare the coefficients directly.
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Hint
Rewrite 6.4 x 10^-5 using 10^-6, then compare it with 8 x 10^-6.
Sample A has concentration 6.4 x 10^-5 and Sample B has concentration 8.7 x 10^-6 grams per gram. How many times larger is 6.4 x 10^-5 than 8 x 10^-6? Use 8 x 10^-6 as an estimate for Sample B's concentration.
Correct. Using the estimate, Sample A's concentration is 8 times as large.
Express both estimated concentrations with the same power of 10 before comparing them.
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Hint
First compare the powers of 10. Then compare coefficients for values with the same power.
Suppose another sample has a concentration of 7.0 x 10^-6 grams per gram. Where would it fall when the concentrations 6.4 x 10^-5, 8.7 x 10^-6, 5.2 x 10^-5, and 7.0 x 10^-6 are ordered from greatest to least?
FirstSecondThirdFourth
Correct. The two 10^-5 values are greatest, and 7.0 x 10^-6 is less than 8.7 x 10^-6.
Values with 10^-5 are greater than these values with 10^-6, and among the 10^-6 values, compare 8.7 and 7.0.
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Meteor Örneklerini İncelemek
TR
ARC_G08_OPS_02_STORY_02
Meteor Örneklerini İncelemek
Searching the Meteor Samples
EN
ARC_G08_OPS_02_STORY_02
Searching the Meteor Samples