On an orbital research station, Emek and Tara discovered that the navigation computer had scrambled its number system map. Five values were waiting to be classified: 14, -7, 3.25, 5/8, and sqrt(11). Emek placed 14 with the natural numbers and noted that it was also an integer and a rational number. Tara classified -7 as an integer and therefore also rational. They recognized that 3.25 and 5/8 were rational because each could be written as a fraction of integers. The final value, sqrt(11), could not be written as such a fraction, so they placed it with the irrational numbers. Tara checked the map's structure: natural numbers belonged inside the integers, and integers belonged inside the rational numbers, while rational and irrational numbers were separate parts of the real numbers. With every value correctly placed, the computer accepted the repaired map and restored the station's navigation calculations.

Challenges

Challenge 1 of 5

Challenges

Challenge 1 of 4
Hint
A rational number can be written as a fraction of two integers. Consider which value cannot be written that way.
Which value from the navigation computer belongs to the irrational numbers?
3.255/8sqrt(11)-7
Correct. Since 11 is not a perfect square, sqrt(11) is irrational.
Check which values can be expressed as ratios of integers and which one cannot.
Next
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Hint
Check each value to see whether it can be written as a fraction of integers.
The computer asks Emek to count how many of the five values 14, -7, 3.25, 5/8, and sqrt(11) are rational numbers. What number should he enter?
Correct. Four of the five values are rational.
Remember that integers, fractions of integers, and terminating decimals are rational numbers.
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Hint
If one number set is contained inside another, a number in the smaller set also belongs to the larger set.
The repaired map shows that natural numbers are inside the integers, and integers are inside the rational numbers. Which statement about the value 14 is therefore correct?
14 is natural but is not an integer.14 is natural, integer, and rational.14 is integer and irrational.14 is rational but is neither natural nor integer.
Correct. Since 14 is natural, it is also an integer and therefore rational.
Follow the nesting of the sets: natural numbers are integers, and integers are rational numbers.
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Sayı Sistemi Haritasını Onarmak
TR
ARC_G09_NUM_02_STORY_01
Sayı Sistemi Haritasını Onarmak
Repairing the Number System Map
EN
ARC_G09_NUM_02_STORY_01
Repairing the Number System Map