Question

directions: without using your calculator, label approximate locations for the following numbers on the number line. note how you approximated each value.
a. $\pi$
b. $-(\frac{1}{2}\cdot\pi)$
hint: $\frac{1}{2}\cdot4$ means $\frac{1}{2}$ of 4.
c. $2\sqrt{2}$
hint: $2 + \frac{1}{2}=2\frac{1}{2}$ so $2+\sqrt{2}=2\sqrt{2}$
d. $\sqrt{17}$

Explanation:

Step1: Approximate \(\pi\)

We know that \(\pi\approx3.14\). So it is a little more than \(3\).

Step2: Approximate \(-(\frac{1}{2}\cdot\pi)\)

First, \(\frac{1}{2}\cdot\pi\approx\frac{1}{2}\times3.14 = 1.57\). Then \(-(\frac{1}{2}\cdot\pi)\approx - 1.57\).

Step3: Approximate \(2\sqrt{2}\)

We know that \(\sqrt{2}\approx1.414\). So \(2\sqrt{2}=2\times1.414 = 2.828\).

Step4: Approximate \(\sqrt{17}\)

We know that \(4^{2}=16\) and \(5^{2}=25\). Since \(17\) is \(1\) more than \(16\), \(\sqrt{17}\approx4.123\).

Answer:

• For \(a\). \(\pi\approx3.14\), mark it a little more than \(3\) on the number - line.
• For \(b\). \(-(\frac{1}{2}\cdot\pi)\approx - 1.57\), mark it between \(-2\) and \(-1\) closer to \(-1.5\) on the number - line.
• For \(c\). \(2\sqrt{2}\approx2.828\), mark it between \(2\) and \(3\) closer to \(2.8\) on the number - line.
• For \(d\). \(\sqrt{17}\approx4.123\), mark it between \(4\) and \(5\) closer to \(4.1\) on the number - line.