Is14/5arationalnumber? Choices: (A)yes (B)no

Understand the nature: Step 1: Understand the nature of 14/5. 14/5 is a fraction where both numerator (14) and denominator (5) are integers. Check decimal form: Step 2: Check if the fraction can be expressed as a terminating or repeating decimal. Since 5 is the only prime factor of the denominator, 14/5 can be expressed as a decimal that either terminates or repeats. Convert to decimal: Step 3: Convert 14/5 to a decimal to further analyze. 14 ÷ 5 = 2.8, which is a terminating decimal. Determine rationality: Step 4: Determine if 14/5 is rational based on its decimal form. A number is rational if it can be expressed as a fraction of two integers or as a terminating or repeating decimal. Since 2.8 is a terminating decimal, 14/5 is a rational number.

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Is $\frac{14}{5}$ a rational 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{14}{5}

a rational number?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Understand the nature: Step $1$ : Understand the nature of $\frac{14}{5}$ . $\frac{14}{5}$ is a fraction where both numerator ( $14$ ) and denominator ( $5$ ) are integers.
Check decimal form: Step $2$ : Check if the fraction can be expressed as a terminating or repeating decimal. $\newline$ Since $5$ is the only prime factor of the denominator, $\frac{14}{5}$ can be expressed as a decimal that either terminates or repeats.
Convert to decimal: Step $3$ : Convert $\frac{14}{5}$ to a decimal to further analyze. $\newline$ $14 \div 5 = 2.8$ , which is a terminating decimal.
Determine rationality: Step $4$ : Determine if $14/5$ is rational based on its decimal form. $\newline$ A number is rational if it can be expressed as a fraction of two integers or as a terminating or repeating decimal. Since $2.8$ is a terminating decimal, $14/5$ is a rational number.