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} $
Conclusion
The decimal 0.875 fits the definition of a Rational Number because it can be represented as the fraction $7/8$.
Similar Questions
- What type of number is the result of multiplying a Rational Number with an Irrational Number?
- Which of these is a number that is real but NOT rational?
- Which of the following numbers is both a Rational Number and a Terminating Decimal?
Important Questions from Rational or Irrational Numbers
If \(\sqrt{1+\frac{\sqrt{3}}{2}}- \sqrt{1-\frac{\sqrt{3}}{2}}= c\) , then the value of c is:
If \(\frac{\sqrt{38-5\sqrt{3} } }{\sqrt{26+7\sqrt{3} } }= \frac{a+b\sqrt{3} }{23} \) , b > 0, then the value of (b – a) is:
If \( \frac{5}{4{\sqrt 2 }} + \frac{{3 + 2\sqrt 2 }}{{3 - 2\sqrt 2 }} - \frac{{3 - 2\sqrt 2 }}{{3 + 2\sqrt 2 }} = a + b\sqrt 2 \) , then what is the value of (3a + 4b)?
If \(\frac {8 + 2\sqrt 3}{3\sqrt 3 + 5} = a\sqrt 3 - b,\) then the value of a + b is equal to:
If \(\frac{\sqrt{26-7\sqrt{3} } }{\sqrt{14+5\sqrt{3} } } = \frac{b+a\sqrt{3} }{11}\) , b > 0, then what is the value of \(\sqrt{(b-a)} \) ?
