Question

directions: use the drawing tool(s) to form the correct answer on the provided number line. consider the following fractions: \\(\frac{7}{6}\\), \\(\frac{8}{3}\\), \\(\frac{9}{4}\\), \\(\frac{11}{9}\\). determine which of the fractions is a terminating decimal number. plot the point representing that fraction on the number line.

Explanation:

Step1: Recall terminating decimal rule

A fraction in simplest form has a terminating decimal if its denominator has prime factors only 2 and/or 5.

Step2: Simplify each fraction

• $\frac{7}{6}$: Denominator $6 = 2\times3$ (has 3, not terminating).
• $\frac{8}{3}$: Denominator $3$ (not 2/5, not terminating).
• $\frac{9}{4}$: Denominator $4 = 2^2$ (only 2, terminating). $\frac{9}{4}=2.25$.
• $\frac{11}{9}$: Denominator $9 = 3^2$ (not 2/5, not terminating).

Step3: Plot $\frac{9}{4}$ on number line

$\frac{9}{4}=2.25$. The number line has 1, 2, 3. Between 2 and 3, divide into 4 parts (since 1 unit from 2 to 3, each part 0.25). 2.25 is 1 part (0.25) after 2.

Answer:

The fraction is $\frac{9}{4}$ (or 2.25), plot the point at 2.25 on the number line.