Is2/3anirrationalnumber? Choices: (A)yes (B)no

Define 2/3: Step 1: Define the number 2/3. 2/3 is a fraction where the numerator is 2 and the denominator is 3. Determine decimal type: Step 2: Determine if 2/3 is a terminating or repeating decimal. When we divide 2 by 3, the decimal 0.666... repeats indefinitely. Define irrational numbers: Step 3: Define irrational numbers. Irrational numbers are numbers that cannot be expressed as a simple fraction and their decimal expansions are non-terminating and non-repeating. Compare with definition: Step 4: Compare 2/3 with the definition of irrational numbers. Since 2/3 is a repeating decimal, it does not fit the definition of an irrational number, which must be non-repeating and non-terminating.

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Is $\frac{2}{3}$ an irrational number? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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Math Problems

Grade 8

Identify rational and irrational numbers

Full solution

Q. Is

\frac{2}{3}

an irrational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Define $\frac{2}{3}$ : Step $1$ : Define the number $\frac{2}{3}$ . $\frac{2}{3}$ is a fraction where the numerator is $2$ and the denominator is $3$ .
Determine decimal type: Step $2$ : Determine if $\frac{2}{3}$ is a terminating or repeating decimal. $\newline$ When we divide $2$ by $3$ , the decimal $0.666\ldots$ repeats indefinitely.
Define irrational numbers: Step $3$ : Define irrational numbers. Irrational numbers are numbers that cannot be expressed as a simple fraction and their decimal expansions are non-terminating and non-repeating.
Compare with definition: Step $4$ : Compare $\frac{2}{3}$ with the definition of irrational numbers. $\newline$ Since $\frac{2}{3}$ is a repeating decimal, it does not fit the definition of an irrational number, which must be non-repeating and non-terminating.