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.