Problem

Question 6 of 25
Identify the two rational numbers.
A. $2.7182818459 \ldots$
B. $2.777777 \ldots$
C. $\sqrt{3}$
D. $-\frac{7}{3}$

Answer

Expert–verified
Hide Steps
Answer

The two rational numbers are \(\boxed{2.777777 \ldots}\) and \(\boxed{-\frac{7}{3}}\).

Steps

Step 1 :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. Therefore, we need to identify which of the given numbers can be expressed as a fraction.

Step 2 :$2.7182818459 \ldots$ - This number is the mathematical constant e, which is an irrational number.

Step 3 :$2.777777 \ldots$ - This number is a repeating decimal, which can be expressed as a fraction, so it is a rational number.

Step 4 :$\sqrt{3}$ - The square root of 3 is an irrational number.

Step 5 :$-\frac{7}{3}$ - This number is already expressed as a fraction, so it is a rational number.

Step 6 :The two rational numbers are \(\boxed{2.777777 \ldots}\) and \(\boxed{-\frac{7}{3}}\).

link_gpt