Show that 0.235555.can be expressed in the form
where p and q are integers and q =/= 0.

Answer and Step-by-step explanation:

Suppose x = 0.2355555... .

Multiply x by 100 and 1000:

100x = 23.5555

1000x = 235.5555

Let's subtract the first equation from the second:

1000x - 100x = 235.5555 - 23.555

Because the decimal part for each goes on forever, we can simply cancel them out in our subtraction statement:

900x = 235 - 23 = 212

Divide both sides by 900:

x = 212/900 = 53/225

Thus, since x = 0.235555..., we know that:

0.23555 = 53/225

Since p = 53 and q = 225 are integers, we have proven that this repeating decimal can be written as a fraction.

~ an aesthetics lover

-50/3 is the final answer! : )

area = length x width

length = 2 x width

32 = 2 x width x width

32 = 2 x width^2

36 = width ^2  

width = 6

length = 12

area is 32

perimeter = 2 x 12 + 2 x 6 = 24 + 12 = 36

step-by-step explanation: