Question

4. Which number produces anirrational answer when multipliedby 0.79?A.B. 0.383838...C. 0.12D.קשותU

Answer 1

Recall that the product between two rational numbers is always a rational number, and the product between an irrational number and a rational number different from zero is always an irrational number.

Also, recall that a rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator p, and a non-zero denominator q.

Now, notice that:

$\begin{gathered} 0.79=\frac{79}{100}, \\ 0.383838\ldots=\frac{38}{99}, \\ 0.12=\frac{12}{100}. \end{gathered}$

Therefore, 0.79, 0.383838..., 0.12 are rational numbers.

Now, recall that:

$\sqrt[]{7}$

is an irrational number.

Therefore, the product between 0.79 and √7 is an irrational number.

Answer: Option A.