Show that each of the decimal numbers below is actually a rational by expressing it as a ratio of two integers.

0.02, 6.23, 2.71828, -168.5, -0.00005

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.

Show that each of the decimal numbers below is actually a rational by expressing it as a ratio of two integers. 0.02, 6.23, 2.71828, -168.5, -0.00005

Discover how to express decimals like 0.02, 6.23, 2.71828, -168.5, and -0.00005 as rational numbers by converting them into fractions. This step-by-step guide covers fundamental concepts from number theory and rational numbers, making it suitable for students in Grades 6-8.

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