Identify each rational number.

   

    Does Not Terminate  

              in Zeros    

 

    Terminates in Zeros   

 

     −4815

 

	
 

     28.178¯¯¯¯¯
  

 

	
 

          15
  

 

	
           

          79
  

 

	
 

        0.200...  

 

	
 

        0.005  

 

	
 

Let's break down each number and categorize it based on whether it terminates in zeros or does not terminate in zeros:

1. **−4815**  
   - This is an integer and a rational number. It **terminates in zeros** because any whole number can be written with zeros after the decimal point (e.g., -4815.000...).

2. **28.178¯¯¯¯¯**  
   - The notation **28.178**¯¯¯¯¯ indicates a repeating decimal, meaning **178** repeats indefinitely. This number **does not terminate in zeros** because it repeats a sequence rather than ending in zeros. However, it's a rational number because repeating decimals are considered rational.

3. **15**  
   - This is another integer and a rational number. It **terminates in zeros** since it can be written as 15.000...

4. **79**  
   - Like the others, this is an integer and a rational number. It **terminates in zeros** because it can be expressed as 79.000...

5. **0.200...**  
   - This is a terminating decimal number. It **terminates in zeros** since the decimal places stop after 0.200.

6. **0.005**  
   - This number also **terminates in zeros**, as it ends at the third decimal place without repeating.

### Summary:
- **Terminates in Zeros**: −4815, 15, 79, 0.200..., 0.005
- **Does Not Terminate in Zeros**: 28.178¯¯¯¯¯ (since it repeats).

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Do you have any questions, or would you like further details on these classifications?

**Related Questions:**
1. What is the difference between repeating decimals and terminating decimals?
2. How do you convert a repeating decimal into a fraction?
3. Why are all integers considered rational numbers?
4. How can you tell if a decimal representation of a number is rational?
5. Are there any irrational numbers in this set?

**Tip:** Any decimal that repeats or terminates is always a rational number because it can be written as a fraction.

Identify each rational number. Does Not Terminate in Zeros, Terminates in Zeros: −4815, 28.178¯¯¯¯¯, 15, 79, 0.200..., 0.005.

Explore how to identify rational numbers and distinguish between decimals that terminate in zeros and those that do not. This example includes integers, repeating decimals like 28.178¯¯¯¯¯, and terminating decimals like 0.200... and 0.005. Suitable for Grades 6-8 students learning about rational numbers.

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