Question

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the number b is rational. which statement about 10·b is true?
10·b is rational.
10·b is irrational.
10·b can be rational or irrational, depending on the value of b.

Explanation:

Step1: Define rational number

A rational number $b$ can be written as $\frac{p}{q}$, where $p,q$ are integers and $q
eq0$.

Step2: Multiply by 10

Calculate $10\cdot b$: $10\cdot b = 10\cdot\frac{p}{q}=\frac{10p}{q}$

Step3: Verify rationality

Since $10p$ and $q$ are integers, and $q
eq0$, $\frac{10p}{q}$ is rational.

Answer:

10 $\cdot$ b is rational.