options: Use complex numbers in polynomial identities and equations.

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

Perform operations on vectors.

Represent complex numbers and their operations on the complex plane.

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

Reason quantitatively and use units to solve problems.

Represent and model with vector quantities.

Use properties of rational and irrational numbers.

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

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

Perform operations on matrices and use matrices in applications.

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

Extend the properties of exponents to rational exponents.

Perform arithmetic operations with complex numbers.
problem_activity: Task
Malia found a "short cut" to find the decimal representation of the fraction $\frac{117}{250}$.  Rather than use long division she noticed that because $250 \times 4 = 1000$,
$$\frac{117}{250} = \frac{117 \times 4}{250 \times 4} = \frac{468}{1000} = 0.468.$$
For which of the following fractions does Malia's strategy work to find the decimal representation?
$$\frac{1}{3}, \frac{3}{4}, -\frac{6}{25}, \frac{18}{7}, \frac{13}{8} \;\; {\rm and} \;\; -\frac{113}{40}.$$
For each one for which the strategy does work, use it to find the decimal representation.
For which denominators can Malia's strategy work?


correct_option_index: 9