How is the number of zeros in the quotient in 180 divided by 8 equals 20 related to the bumber zeros in the dividen?

Be sure to proofread your questions before you post them.

First of all, 180/8 ≠ 20, 180/8 = 22.5

Do you mean 180/9 = 20?

The more zeros in the dividend, all other things being equal, the more in the quotient.

1800/9 = 200
18,000/9 = 2000

The number of zeros in the quotient of 180 divided by 8 being 20 is related to the number of zeros in the dividend through the concept of place value.

To understand this relationship, let's break down the process of division:

1. Dividend: The number that is being divided, in this case, 180.
2. Divisor: The number we are dividing by, in this case, 8.
3. Quotient: The result of the division, in this case, 20.

When we perform the division operation, we divide each digit of the dividend starting from the left, working our way to the right. In this case, we start with the digit "1" of the dividend, and we find that 1 ÷ 8 equals 0 with a remainder of 1.

Since the divisor (8) is larger than the dividend (1), we add a zero to the quotient:

0
_______
8 | 1 8 0
- 0
------
1

Next, we bring down the next digit "8" from the dividend and divide it by the divisor:

0
_______
8 | 1 8 0
- 0
------
8

Now, we can see that 8 ÷ 8 equals 1. So, we place "1" in the quotient, which brings us to:

0
_______
8 | 1 8 0
- 0 8
------
12

Now, when we look at the remaining part of the dividend, which is 12, we have two digits. The division process continues with the next digit "1" in the dividend, and we find that 12 ÷ 8 equals 1 with a remainder of 4.

0 1
_______
8 | 1 8 0
- 0 8
------
1 2
0

We add the result "1" to the quotient, giving us:

0 1
_______
8 | 1 8 0
- 0 8
------
1 2
- 0 8
------
4

Finally, we have the remainder "4" left, and since there are no more digits in the dividend to bring down, the division process is complete.

The relationship between the number of zeros in the quotient (20) and the number of zeros in the dividend (180) lies in the place value system. In this case, the dividend has two zeros, and accordingly, the quotient has the same number of zeros at the end.

So, whenever there is a zero at the end of a number being divided, it will result in a zero at the end of the quotient.