options: Reason quantitatively and use units to solve problems.

Extend the properties of exponents to rational exponents.

Represent complex numbers and their operations on the complex plane.

Perform arithmetic operations with complex numbers.

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

Perform operations on vectors.

Represent and model with vector quantities.

Know that there are numbers that are not rational, and approximate them by rational numbers.

Apply and extend previous understandings of numbers to the system of rational numbers.

Use complex numbers in polynomial identities and equations.

Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

Compute fluently with multi-digit numbers and find common factors and multiples.

Perform operations on matrices and use matrices in applications.

Use properties of rational and irrational numbers.
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)?


correct_option_index: 4