show that the following recurring decimals are rational.
(1) 0,14 (the dot is on the 4)
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.