Question

2.08 partner practice

1. if $\frac{1}{9}=.overline{1}$, what is the meaning of the vinculum, or the bar above the 1?
2. convert the fraction $\frac{2}{3}$ into a decimal and determine if it is terminating or repeating.
3. convert the fraction $-\frac{3}{12}$ into a decimal and determine if it is terminating or repeating.

Explanation:

Step1: Define vinculum meaning

The vinculum (bar) over a digit in a decimal indicates that the digit repeats infinitely.

Step2: Convert $\frac{2}{3}$ to decimal

$2\div3 = 0.\overline{6}$, it is a repeating - decimal.

Step3: Simplify and convert $-\frac{3}{12}$ to decimal

First, simplify $-\frac{3}{12}=-\frac{1}{4}$. Then, $- 1\div4=-0.25$, it is a terminating decimal.

Answer:

1. The vinculum over a digit in a decimal means the digit repeats infinitely.
2. $\frac{2}{3}=0.\overline{6}$, it is a repeating decimal.
3. $-\frac{3}{12}=-\frac{1}{4}=-0.25$, it is a terminating decimal.