Question

Which of the following statements explains why 0.8 is or is not a rational number?

A. 0.8 is rational because it can be written as a ratio of two integers, 8/9.
B. 0.8 is rational because it can be written as a ratio of two integers, 8/10.
C. 0.8 is irrational because it can be written as a ratio of two integers, 8/9.
D. 0.8 is irrational because it can be written as a ratio of two integers, 8/10.

Answer 1

0.8 is a rational number because it can be expressed as a ratio of two integers, specifically 8/10 which simplifies to 4/5. Option B is the correct statement.

Step-by-step explanation:

The statement that explains why 0.8 is a rational number is B. 0.8 is rational because it can be written as a ratio of two integers, 8/10. A rational number is defined as a number that can be expressed as the division of two integers, where the numerator is an integer and the denominator is a nonzero integer. The fraction 8/10 is an example of such a ratio, which simplifies to 4/5. Both numerator and denominator are integers, and the denominator is not zero, which classifies 0.8 as a rational number.

Statements A and C incorrectly identify 8/9 as equivalent to 0.8, which it is not. Statement D mistakenly labels the number as irrational even though it presents the correct fraction that represents 0.8.