As Emek and Tara approached an unexplored planet, their scanner received five measurements: 7/8, 1.375, 0.272727..., sqrt(36), and sqrt(13). Before the landing computer could use them, each value had to be placed on its number system map. Tara rewrote 1.375 as 11/8, confirming that it was rational. Emek recognized that 0.272727... repeated the same two digits and could be written as 3/11, so it was rational too. The fraction 7/8 was already clearly rational. Next, they simplified sqrt(36) to 6, making it a natural number, an integer, and a rational number. But 13 was not a perfect square, so sqrt(13) was irrational. They checked that every value was also a real number and sent the completed classifications to the landing computer. The scanner accepted the organized signals, calculated a safe approach, and guided their spacecraft toward the planet's surface.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
A terminating decimal and a repeating decimal can both be written as fractions of integers.
Which pair of scanner measurements shows two different decimal forms that are both rational numbers?
1.375 and 0.272727...1.375 and sqrt(13)0.272727... and sqrt(13)sqrt(36) and sqrt(13)
Correct. Both the terminating decimal 1.375 and the repeating decimal 0.272727... are rational.
Look for the terminating decimal and the repeating decimal that can each be written as a fraction of integers.
Next
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Hint
Classify each value as rational or irrational, then remove any rational value that is also an integer.
The landing computer counts how many of the five measurements 7/8, 1.375, 0.272727..., sqrt(36), and sqrt(13) are rational but not integers. How many measurements should it count?
Correct. Three measurements are rational numbers that are not integers.
First identify the four rational values, then check which of those is an integer.
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Hint
First simplify sqrt(49), then classify the resulting number in all sets to which it belongs.
The scanner receives one additional measurement, sqrt(49). Based on how Emek and Tara classified sqrt(36), where should sqrt(49) be placed on the number system map?
Irrational and real onlyRational and real, but not an integerInteger and rational, but not naturalNatural, integer, rational, and real
Correct. sqrt(49) equals 7, which is natural, integer, rational, and real.
Simplify sqrt(49) first, then follow the number system relationships from natural numbers to real numbers.
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Bilinmeyen Gezegenden Gelen Sinyaller
TR
ARC_G09_NUM_02_STORY_02
Bilinmeyen Gezegenden Gelen Sinyaller
Signals from the Unknown Planet
EN
ARC_G09_NUM_02_STORY_02
Signals from the Unknown Planet