Finding the Decimal Equivalent of 13 / -11: A Step-by-Step Division Guide for Math Enthusiasts

What is the decimal equivalent to 13 / -11?

To find the decimal equivalent of 13 / -11, we need to divide 13 by -11

To find the decimal equivalent of 13 / -11, we need to divide 13 by -11.

When dividing a positive number (13 in this case) by a negative number (-11), the result will be negative.

To perform the division, we can set it up as follows:

-1
_________________
-11 | 13

To start the division, we ask ourselves, “How many times does -11 go into 13?”

Since -11 is smaller than 13, it can only go in once. We write 1 above the line.

-1
_________________
-11 | 13

1

Next, we multiply -11 by 1, and subtract the result from 13:

-1
_________________
-11 | 13

1
_________________
11
-11
_________________
2

We have a remainder of 2.

To continue the division process, we bring down the next digit, which is 0 since there is no other number after 13.

-1.1
_________________
-11 | 13.0

1
_________________
11
-11
_________________
2

2
_________________
20

Now we ask, “How many times does -11 go into 20?”

Since -11 is smaller than 20, it can go in once. We write 1 after the decimal point.

-1.1
_________________
-11 | 13.0

1
_________________
11
-11
_________________
2

2
_________________
20
– 11
_________________
9

We have a remainder of 9.

Since we want to find the decimal equivalent, we can continue adding zeroes after the decimal point and dividing by -11 until we achieve the desired level of accuracy or until the division no longer produces significant digits.

Thus, we can continue the division as:

-1.1…
_________________
-11 | 13.0…

1
_________________
11
-11
_________________
2

2
_________________
20
– 11
_________________
9

0
0
_________________
90
– 88
_________________
2

This pattern repeats as 2 / -11 = 0.181818…

So, the decimal equivalent of 13 / -11 is approximately -1.181818… (repeating).

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