Is a product of two positive decimals less than 1 always less than each of the decimals? Justify your answer.
Choose the correct answer below.
A. Yes. Suppose the decimals are x and y. Since terminating decimals are rational numbers, inequalities for decimals have the same properties as inequalities among rationals. If 0
multiply both sides of the inequality by y to get 0<xy <y. Similarly, 0<xy <x.
B. Yes. Suppose the decimals are x and y. Since terminating decimals are whole numbers, inequalities for decimals have the same properties as inequalities among whole numbers
0<x<1, multiply both sides of the inequality by y to get 0<xy <y. Similarly, 0<xy <?.
C. No. Suppose the decimals are x and y. Since terminating decimals are not rational numbers, inequalities for decimals have different properties from inequalities among rationals.
D. No. Suppose the decimals are x and y. Since terminating decimals are rational numbers, inequalities for decimals have the same properties as inequalities among rationals. If 0<
multiply both sides of the inequality by y to get y <xy <2y. Similarly, x <xy <2x.