What is 1.024242424 as a fraction?

Answer 1

To convert the decimal 1.024242424 into a fraction, first express the repeating part separately. The decimal can be written as 1 + 0.024242424. Let ( x = 0.024242424 ). Multiplying by 1000 gives ( 1000x = 24.242424 ), and multiplying by 100 gives ( 100x = 2.42424 ). Subtracting these two equations results in ( 900x = 21.81818 ), so ( x = \frac{21.81818}{900} ). The repeating part can be simplified to ( \frac{24}{990} ), which reduces to ( \frac{12}{495} ). Adding 1 gives ( 1 + \frac{12}{495} = \frac{495 + 12}{495} = \frac{507}{495} ). Thus, 1.024242424 as a fraction is ( \frac{507}{495} ).