jayne uses long division to convert a rational number $\frac{a}{b}$ to a decimal. which of the following…

jayne uses long division to convert a rational number $\frac{a}{b}$ to a decimal. which of the following statements cannot be true? the decimal form of $\frac{a}{b}$ terminates in zeros. the decimal form of $\frac{a}{b}$ eventually repeats. the decimal form of $\frac{a}{b}$ is a whole number. the decimal form of $\frac{a}{b}$ never repeats or terminates.

jayne uses long division to convert a rational number $\frac{a}{b}$ to a decimal. which of the following statements cannot be true? the decimal form of $\frac{a}{b}$ terminates in zeros. the decimal form of $\frac{a}{b}$ eventually repeats. the decimal form of $\frac{a}{b}$ is a whole number. the decimal form of $\frac{a}{b}$ never repeats or terminates.

Answer

Answer:

D. The decimal form of $\frac{a}{b}$ never repeats or terminates.

Explanation:

Step1: Recall definition of rational numbers

A rational number $\frac{a}{b}$ ($b\neq0$) can be written as a terminating decimal (e.g., $\frac{1}{2}=0.5$) when the denominator $b$ has only factors of 2 and 5 in its prime - factorization.

Step2: Recall repeating decimals

It can also be written as a repeating decimal (e.g., $\frac{1}{3}=0.\overline{3}$) when the denominator has prime factors other than 2 and 5.

Step3: Consider whole - number case

If $b$ divides $a$ evenly, $\frac{a}{b}$ is a whole number (e.g., $\frac{4}{2} = 2$).

Step4: Analyze non - repeating non - terminating case

Non - repeating non - terminating decimals are irrational numbers. Since $\frac{a}{b}$ is a rational number, it cannot be a non - repeating non - terminating decimal.