Question

One way to show that the number -0.33 is rational is to show that -0.33 = x/y, where x and y are integers and y is non-zero. Select a pair of values for x and y to show that -0.33 is rational.

a. x = 33, y = 100 b. x = 33, y = -100 c. x = 100, y = 33 d. x = 100, y = -33

Answer 1

To show -0.33 as a rational number, we select the pair of values x = 33 and y = -100, which when divided, equal -0.33, confirming that it is indeed a rational number.

Step-by-step explanation:

The question at hand involves demonstrating that the number -0.33 is rational by expressing it as a fraction x/y, where x and y are integers, and y is non-zero. To do this, one must select a pair of values for x and y that equate to -0.33 when divided.

Examining the options given, we can exclude option c (x = 100, y = 33) and option d (x = 100, y = -33) because neither ratio (-0.33) equals 100/33 or -100/33. Instead, we look at options a (x = 33, y = 100) and b (x = 33, y = -100), which are closer approximations of -0.33.

The correct answer is b. x = 33, y = -100. This is because when the numerator (x) is positive and the denominator (y) is negative, the resulting fraction is negative. The ratio 33/-100 simplifies to -0.33, thus confirming that -0.33 is rational since it can be expressed as the division of two integers where y is not zero.