Question

1. a roller coaster dives to a depth of $2\frac{3}{16}$ meters below sea level.

part a: write the decimal equivalent to $-2\frac{3}{16}$.
a) 2.19
b) $-2.1\overline{8}$
c) $-2.1875$
d) $-2.\overline{187}$
part b: the decimal is repeating/terminating (circle one)

1. simplify $\pm\sqrt{\frac{25}{81}}$. select all that apply.
2. simplify $\pm\sqrt{\frac{4}{81}}$. select all that apply.
3. simplify $\pm\sqrt{\frac{16}{81}}$. select all that apply.

a) $-\frac{2}{3}$
b) $-\frac{4}{9}$
c) $\frac{4}{9}$
d) $-0.444...$
e) $0.999...$
f) 0.444

Explanation:

Step1: Convert mixed number to improper fraction

$$-2\frac{3}{16}=-\frac{2\times16 + 3}{16}=-\frac{35}{16}$$

Step2: Divide numerator by denominator

$$-\frac{35}{16}=-35\div16=-2.1875$$

Step3: Determine decimal type

Since the division of \(35\) by \(16\) results in a finite number of decimal places (\(-2.1875\)), it is a terminating decimal.

Step4: Simplify \(\pm\sqrt{\frac{16}{81}}\)

Using the property \(\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}\) (\(a = 16\), \(b=81\)), we have \(\pm\sqrt{\frac{16}{81}}=\pm\frac{\sqrt{16}}{\sqrt{81}}=\pm\frac{4}{9}\). \(-\frac{4}{9}=- 0.444\cdots\) and \(\frac{4}{9}=0.444\cdots\)

Answer:

Part A: C. \(-2.1875\)
Part B: terminating
For \(6\): B. \(-\frac{4}{9}\), C. \(\frac{4}{9}\), D. \(-0.444\cdots\)