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.

answer: b.

step-by-step explanation:

it is b. cause the equations are put in the right category

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0