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How many integers are there on the number line between $\dfrac{17}{3}$ and $\left(\dfrac{17}{3}\right)^2$?

 Apr 8, 2020
 #1
avatar+34 
-1

\(\frac{17}{3}\approx6\)

\((\frac{17}{3})^2\approx32\)

 

\(32-6=26\)

 

There are 26 integers between \(\frac{17}{3}\) and \((\frac{17}{3})^2\)

 

-Ako

 Apr 8, 2020
 #2
avatar+50 
+1

Ako, I understand your process, but the last part of arithmetic is wrong. 

 

We know that the first term in the sequence in numbers between is 17/3 which's ceiling is 6, and (17/3)^2, which's floor is 32. 

 

The sequence is as follow: 

(6, 7, 8, ...., 30, 31, 32)

 

So we have to find the number of terms between 6 and 32 inclusive, which is 32 - 6 + 1 and that is 27, we have to do this because subtraction only includes 1 of the values not both of them. 

 

Or we could've done it by subtracting 5 from every term in the sequence then you would get:

(6-5, 7-5, 8-5, ...., 30-5, 31-5, 32-5)

(1, 2, 3, ..., 25, 26, 27)

 

Either way you can see that there are 27 terms, so the answer is 27 integers. smiley

KingHTML  Apr 8, 2020

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