Activities

1. Define terminating decimal and identify one example.
   
   
2. Define repeating decimal and identify one example.
   
   
3. Write 0.24 as a fraction in simplest form.
   
   
4. Write as a fraction in simplest form.
   
   
5. Convert -2.005 to a mixed number in simplest form.
   
   
6. Convert 8.024024024… to a mixed number in simplest form.

7. For each decimal, find three equivalent fractions, if possible.
   1. 0.4
   2. 0.4444…
   3. 0.14144144414444…

8. Complete the table by converting each of the following decimals to fractions.  Do not simplify. 

1. Explain a pattern you see.
2. Predict if your pattern will work on the repeating decimal 0.1777…
3. Convert 0.1777… to a fraction.  Was your prediction correct? Why or why not?

Answer Key/Rubric

1. Terminating decimals are decimals with a finite number of digits, the decimal ends.
   Acceptable examples might include, but are not limited to:  0.25, -2.4, 3.13468

2. Repeating decimals are decimals that have a digit or a group of digits that repeat over and over forever, without end.
   Acceptable examples might include, but are not limited to:

7. Acceptable answers might include, but are not limited to:
   
   
   1. 
   2. 
   3. Not possible.  This decimal is an irrational number as it is nonterminating and nonrepeating and therefore cannot be written as a fraction.

8. See table for answers:

1. Acceptable responses might include, but are not limited to:

• The number of digits repeating determines the number of 9’s in the denominator
• The digits that repeat become the numerator

2. Student makes a reasonable prediction.
3. Answer should be: , so it does not follow the pattern. Student accurately assesses their prediction and justifies why or why not it was correct.