Question

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Part 1
Error Analysis  Elijah says that 3.78778777 font size decreased by 4 . font size decreased by 4 . font size decreased by 4 . is a rational number. Deena disagrees and says the number is irrational. Decide who is correct and what might likely cause one of them to make the error.
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Part 1
Who is​ correct? What might likely cause one of them to make the​ error?
A.
Both Elijah and Deena are correct. Numbers like this one are both rational and irrational.
B.
Elijah is correct. Deena may see 3.78778777 font size decreased by 4 . font size decreased by 4 . font size decreased by 4 . as not showing a repeating pattern.
C.
Deena is correct. Elijah may see 3.78778777 font size decreased by 4 . font size decreased by 4 . font size decreased by 4 . as showing a repeating pattern.
D.
Neither is correct. The number cannot be classified as rational or irrational.

Answer 1

B.

Elijah is correct. The decimal 3.787787787... has a repeating block (78), so it is a repeating decimal and therefore rational (for example 3.\overline{78} = 125/33). Deena’s mistake likely comes from not recognizing the repeating pattern (or from misreading a messy/poorly formatted decimal), so she thought it was nonrepeating and therefore irrational.