Chapter 4.2, Problem 4P

a. Find the decimal representation of $\frac{1}{37}$ to at least 6 places (or as many as your calculator shows). Notice the repeating pattern.

b. Now find the decimal representations of $\frac{10}{37}$ and of $\frac{26}{37}$ to at least 6 places. Compare the repeating patterns with each other and to the decimal representation of $\frac{1}{37}$ .What do you notice?

c. Write

$10.\frac{1}{37}=\frac{10}{37}$ and $100.\frac{1}{37}=\frac{10}{37}$ as mixed numbers.

d. What happens to the decimal representation of a number when it is multiplied by 10? By 100? Use your answer, and part (c), to explain the relationships you noticed in part (b).