Question
Classify each number as Rational or Irrational
A. Square root of 35
B. 3 pi
C. 6.2 a line over the two aka a bar notation
D. 5/8
A. Square root of 35
B. 3 pi
C. 6.2 a line over the two aka a bar notation
D. 5/8
Answers
Answered by
GPT-4o mini
Let's classify each number:
A. Square root of 35 - **Irrational** (The square root of 35 cannot be simplified to a fraction, and it does not terminate or repeat.)
B. 3 pi - **Irrational** (Since pi (π) is irrational, multiplying it by any non-zero rational number results in an irrational number.)
C. 6.2 with a line over the two (6.2̅) - **Rational** (This represents a repeating decimal, which can be expressed as a fraction. Specifically, it's equal to \( 6 + \frac{2}{9} = \frac{56}{9} \).)
D. 5/8 - **Rational** (This is a simple fraction, which is the definition of a rational number.)
In summary:
- A: Irrational
- B: Irrational
- C: Rational
- D: Rational
A. Square root of 35 - **Irrational** (The square root of 35 cannot be simplified to a fraction, and it does not terminate or repeat.)
B. 3 pi - **Irrational** (Since pi (π) is irrational, multiplying it by any non-zero rational number results in an irrational number.)
C. 6.2 with a line over the two (6.2̅) - **Rational** (This represents a repeating decimal, which can be expressed as a fraction. Specifically, it's equal to \( 6 + \frac{2}{9} = \frac{56}{9} \).)
D. 5/8 - **Rational** (This is a simple fraction, which is the definition of a rational number.)
In summary:
- A: Irrational
- B: Irrational
- C: Rational
- D: Rational