A rational number in its lowest form has denominator . How many decimal places will its decimal expansion have? Explain your answer.
Explanation:
Let the rational number be .
The decimal expansion of a rational number \(\frac{p}{q}\), where \(q≠0\) in its lowest form will be terminating when the prime factors of \(q\) are (is) .
Thus, the highest power of in the determines the number of decimal places.
First, we need to make the powers of \(2\) and \(5\) .
So, multiply the numerator and the denominator of the considered rational number by .
Thus, we get .
Therefore, the number of decimal places in the decimal expansion of the considered rational number is .