standard_description: Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
problem_activity: Task
Use long division to find the repeating decimal that represents $\frac{29}{13}$
Take the number obtained by including only the first two digits after the decimal point, and multiply that by $13$.
Take the number obtained by including only the first four digits after the decimal point, and multiply that by $13$.
Take the number obtained by including only the first six digits after the decimal point, and multiply that by $13$.
What do you notice about the product of $13$ and decimal approximations of $\frac{29}{13}$ as more and more digits are included after the decimal point?
How does what you observed in Part (e) help make sense of what it means for $\frac{29}{13}$ to be equal to the repeating decimal expression you found in the Part (a)?


aligns: no