Question

4 which number is a rational number that can be converted into a fraction?
a -6.153638...
b 0.59̅
c -4π
d √7

Explanation:

Step1: Recall rational - number definition

A rational number can be written as a fraction $\frac{p}{q}$ where $p,q$ are integers and $q
eq0$. A non - terminating repeating decimal is rational, while non - repeating non - terminating decimals, $\pi$ and square roots of non - perfect squares are irrational.

Step2: Analyze option A

$-6.153638...$ is a non - repeating non - terminating decimal, so it is irrational.

Step3: Analyze option B

$0.5\overline{9}$ is a non - terminating repeating decimal. Let $x = 0.5999\cdots$. Then $10x=5.999\cdots$ and $100x = 59.999\cdots$. Subtracting $10x$ from $100x$ gives $100x-10x=59.99\cdots - 5.99\cdots$, $90x = 54$, $x=\frac{54}{90}=\frac{3}{5}$, so it is rational.

Step4: Analyze option C

Since $\pi$ is irrational, $- 4\pi$ is also irrational.

Step5: Analyze option D

$\sqrt{7}$ is the square root of a non - perfect square, so it is irrational.

Answer:

B. $0.5\overline{9}$