Question

classify the decimal form of each number as terminating, repeating, or neither.
repeating
terminating
neither
√121
5/7
circumference of a circle with radius 5
1/3
π
perimeter of a square with area 16
2/5
√7

Explanation:

Step1: Analyze $\sqrt{121}$

$\sqrt{121}=11$, its decimal form is $11.0$, which is terminating.

Step2: Analyze $\frac{5}{7}$

When we divide 5 by 7, $5\div7 = 0.714285714285\cdots$, it is repeating.

Step3: Analyze circumference of a circle with radius 5

The formula for the circumference of a circle is $C = 2\pi r$. With $r = 5$, $C=10\pi$. Since $\pi$ is non - repeating non - terminating, $10\pi$ is neither terminating nor repeating.

Step4: Analyze $\frac{1}{2}$

$1\div2=0.5$, it is terminating.

Step5: Analyze $\pi$

$\pi=3.1415926535\cdots$ is non - repeating non - terminating, so it is neither.

Step6: Analyze perimeter of a square with area 16

If the area of a square is 16, then the side length $s=\sqrt{16} = 4$, and the perimeter $P = 4s=16$, its decimal form is $16.0$, which is terminating.

Step7: Analyze $\frac{2}{5}$

$2\div5 = 0.4$, it is terminating.

Step8: Analyze $\sqrt{7}$

$\sqrt{7}=2.645751311\cdots$ is non - repeating non - terminating, so it is neither.

Answer:

Repeating: $\frac{5}{7}$
Terminating: $\sqrt{121},\frac{1}{2}$, Perimeter of a square with area 16, $\frac{2}{5}$
Neither: Circumference of a circle with radius 5, $\pi,\sqrt{7}$