Fractions in the simplest form that have denominators of 2, 4,8,16, and 32 produce terminating decimals. fractions with denominators of 6,12,18, and 24 produce repeating decimals. what causes the difference? explain.

Fractions having a denominator which can be factored in terms of 2 or 5 (or both) will terminate completely or will have terminating decimals.  

But the fractions whose denominator can'not be factored only in terms of 2, 5 or both, will repeat or will have repeating decimals..

As 2= , 4= , 8= , 16=

and 32.

Here, 2,4,8,16, and 32 are all powers of 2 and fractions with these denominators will have terminating decimal expansion.  

As,

, , ,

But 6,12, 18, and 24 can'not be factored only in terms of 2 or 5 or both. Therefore, fractions with these denominators will have repeating decimals.

goog may have it for you

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents