Converting -9/75 into a non-terminating decimal

To convert a fraction into a non-terminating decimal, we need to divide the numerator by the denominator. In this case, we have -9 as the numerator and 75 as the denominator. Let's follow the steps below to convert -9/75 into a non-terminating decimal.

Step 1: Divide the numerator by the denominator
When we divide -9 by 75, we get a quotient and a remainder. The quotient represents the whole number part of the decimal, and the remainder helps us determine the fractional part.

Step 2: Divide the remainder by the denominator
To find the fractional part, we take the remainder obtained in step 1 and divide it by the denominator again.

Step 3: Continue dividing until a pattern emerges
We repeat step 2 until a pattern emerges or until we have obtained the desired level of precision.

Now let's apply these steps to convert -9/75 into a non-terminating decimal.

Step 1: Divide -9 by 75
-9 ÷ 75 = -0.12

The quotient is -0.12.

Step 2: Divide the remainder by the denominator
To find the fractional part, we need to multiply the remainder (which is -9) by 10 and divide it by the denominator (which is 75).

(-9 × 10) ÷ 75 = -1.2

The fractional part is -1.2.

Step 3: Continue dividing
To obtain more decimal places and check for patterns, we repeat step 2:

(-1.2 × 10) ÷ 75 = -0.16

(-0.16 × 10) ÷ 75 = -0.02133...

If we continue this process, we will find that the decimal representation of -9/75 does not terminate and forms a repeating pattern of 02133.

Therefore, -9/75 as a non-terminating decimal is -0.1202133...