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A fraction, when converted to a decimal, will do one of two things:
- Terminate (red means stop)
- The decimals stop at some point.
- Not Terminate (green means go)
- The decimals go on forever, like the crazy fools they are.
Examples (Terminating)
$$\frac{1}{2}=0.5$$
$$\frac{5}{16}=0.3125$$
Examples (Non-Terminating)
$$\frac{1}{3}=0.3333...$$
$$\frac{2}{7}=0.285714...$$
It's Not Just Fractions
Irrational numbers are also non-terminating. Take any irrational number and its decimals will go on forever. Look at the two examples below:
$$\pi = 3.141592653589...$$
$$\sqrt{2}=1.414213562373...$$