To show that each of the given decimal numbers is rational, we need to express each one as a ratio (or fraction) of two integers. A rational number can always be written in the form $\frac{a}{b}$, where $a$ and $b$ are integers, and $b \neq 0$.

Let's go through each decimal number:

1. $0.02$

   • $0.02$ can be written as $\frac{2}{100}$.
   • Simplifying: $\frac{2}{100} = \frac{1}{50}$.
   • So, $0.02 = \frac{1}{50}$, which is a ratio of two integers.

2. $6.23$

   • $6.23$ can be written as $\frac{623}{100}$ (since there are two digits after the decimal point).
   • So, $6.23 = \frac{623}{100}$, which is a ratio of two integers.

3. $2.71828$

   • $2.71828$ can be written as $\frac{271828}{100000}$ (since there are five digits after the decimal point).
   • So, $2.71828 = \frac{271828}{100000}$, which is a ratio of two integers.

4. $-168.5$

   • $-168.5$ can be written as $\frac{-1685}{10}$ (since there is one digit after the decimal point).
   • So, $-168.5 = \frac{-1685}{10}$, which is a ratio of two integers.

5. $-0.00005$

   • $-0.00005$ can be written as $\frac{-5}{100000}$.
   • So, $-0.00005 = \frac{-5}{100000}$, which is a ratio of two integers.

Thus, all the given decimal numbers are rational, as they can each be expressed as the ratio of two integers.

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Would you like further details or clarifications?

Here are 5 related questions to explore:

1. How do you convert repeating decimals into rational numbers?
2. What is the difference between rational and irrational numbers?
3. Can a terminating decimal always be written as a rational number?
4. How would you simplify fractions to their lowest terms?
5. How can negative decimal numbers be converted into rational numbers?

Tip: When converting a decimal to a fraction, count the number of decimal places to determine the power of 10 to use in the denominator.