Classifying the Decimal 0.875

The question asks to classify the decimal number 0.875. We need to determine which category it best fits into: Whole Number, Irrational Number, Integer, or Rational Number.

Understanding Number Classifications

• Whole Numbers: These are non-negative integers (0, 1, 2, 3, ...).
• Integers: These include positive and negative whole numbers, including zero (... -2, -1, 0, 1, 2, ...).
• Rational Numbers: Numbers that can be expressed as a fraction $p/q$, where $p$ and $q$ are integers and $q \neq 0$. Their decimal representations either terminate or repeat.
• Irrational Numbers: Numbers that cannot be expressed as a simple fraction $p/q$. Their decimal representations are non-terminating and non-repeating.

Analyzing the Decimal 0.875

Let's analyze the decimal 0.875:

• Is it a Whole Number? No, because it is less than 1 and has a decimal part.
• Is it an Integer? No, because it is not a whole number and has a decimal part.
• Is it an Irrational Number? No, because its decimal representation terminates (it ends after the '5'). Irrational numbers have decimals that go on forever without repeating.
• Is it a Rational Number? Yes. A number is rational if it can be written as a fraction $p/q$. The decimal 0.875 terminates, which means it can be easily converted to a fraction.
  • $0.875 = \frac{875}{1000}$
  • This fraction can be simplified. Divide both numerator and denominator by 125: $ \frac{875 \div 125}{1000 \div 125} = \frac{7}{8} $
  Since 0.875 can be expressed as the fraction $7/8$, where 7 and 8 are integers and 8 is not zero, it is a Rational Number.

Conclusion

The decimal 0.875 fits the definition of a Rational Number because it can be represented as the fraction $7/8$.