show that the following recurring decimals are rational.

Question

(1) 0,14 (the dot is on the 4)

Answer 1

To show that the recurring decimal 0.14 is rational, we need to express it as a fraction, where the numerator and denominator are both integers.

Let x = 0.14
Multiplying both sides by 100 (to shift the decimal point):
100x = 14

Rearranging the equation, we have:
x = 14/100

Simplifying the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
x = 7/50

Therefore, the recurring decimal 0.14 is rational because it can be expressed as the fraction 7/50.