This exercise involves writing repeating decimals in a compact form using bar notation to denote repeating digits.

Let’s rewrite the numbers using bar notation:

1. $3.\overline{9}$
2. $2.\overline{21}$
3. $0.\overline{36}$
4. $4.\overline{34}$
5. $0.\overline{580}$
6. $6.\overline{13434}$
7. $0.\overline{623131}$
8. $0.\overline{123123}$
9. $-1.\overline{2333}$
10. $-3.\overline{24545}$
11. $-1.\overline{525252}$
12. $-1.\overline{020202}$
13. $-6.\overline{676767}$
14. $-23.\overline{0232323}$
15. $-5.\overline{02121}$
16. $-0.\overline{01919}$

Here:

• The digits under the bar (e.g., $\overline{36}$) represent the repeating section.
• The repeating block of digits may vary in length.

Do you want me to explain how to convert repeating decimals to fractions or provide further details?

Here are 5 follow-up questions to expand on the topic:

1. How do you convert $0.\overline{3}$ into a fraction?
2. What is the process for turning repeating decimals into mixed numbers?
3. Can you explain how to identify the repeating sequence in a decimal?
4. How do repeating decimals appear when expressed as fractions?
5. Why do some decimals terminate while others repeat?

Tip: For $x = 0.\overline{36}$, you can multiply $x$ by a power of 10 to "shift" the repeating part, helping to solve for $x$ as a fraction.