Show that the following decimals are rational.

Question

(1) 0,124 (the dot is on 1 and 4)
(2) -1,124(the dot is on 2 and 4)
(3) -2,35(the dot is on 5)

Answer 1

To show that a decimal is rational, we need to demonstrate that it can be written as a fraction of two integers.

(1) 0,124 = 124/1000 = 31/250
Thus, 0,124 is rational.

(2) -1,124 = -1124/1000 = -281/250
Thus, -1,124 is rational.

(3) -2,35 = -2 - 35/100 = -2 - 7/20 = -2 - 7/20 = -47/20
Thus, -2,35 is rational.