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

Guest Apr 8, 2020

#1**-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

Ako180 Apr 8, 2020

#2**+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. **

KingHTML
Apr 8, 2020