What is 1.024242424 In a fraction?

Answer 1

The decimal 1.024242424... can be expressed as a fraction. By letting ( x = 1.024242424... ), we can isolate the repeating part. Multiplying by 100 (to shift the decimal point two places) gives ( 100x = 102.424242424... ). Subtracting the original equation from this yields ( 99x = 101.4 ), leading to ( x = \frac{1014}{990} ) when simplified, which reduces to ( \frac{507}{495} ) or further to ( \frac{169}{165} ). Thus, ( 1.024242424... = \frac{169}{165} ).