How to Divide a Number by 99

Here is the divisibility rules for 99 tutorial which helps you in knowing how to divide a number by 99. Also, you can refer the table that shows fraction and reciprocal for the numbers from 1 to 20 on dividing by 99. Refer below example problems to get a clear idea of how to divide a number by 99.

Divisibility Rules for 99 Tutorial

Number Fraction Reciprocal
1 1/99 0.010101
2 2/99 0.020202
3 3/99 0.030303
4 4/99 0.040404
5 5/99 0.050505
6 6/99 0.060606
7 7/99 0.070707
8 8/99 0.080808
9 9/99 0.090909
10 10/99 0.101010
11 11/99 0.111111
12 12/99 0.121212
13 13/99 0.131313
14 14/99 0.141414
15 15/99 0.151515
16 16/99 0.161616
17 17/99 0.171717
18 18/99 0.181818
19 19/99 0.191919
20 20/99 0.202020


Try to observe the pattern in the reciprocals. The reciprocal of any number divided by 99 is equal to just repeating the number itself. So, 56/99 = 0.56565656.

With this understanding, let us understand this mathematical shortcut of dividing any number by 99 with a simple example. To begin with, let us consider a 3-digit number.


Dividing a 3-digit number

Example 1: Find 964 / 99.

Solution : Step 1 : Here 964 is the dividend and 99 is the divisor. In this example, divisor(99) has 2 digit. So, set 2 digit from right as reminder. Group the digits on the left into groups of 2.

Step 2 : The quotient is just the digit on the left. In our case, it is 9. So, the quotient is 9.

Step 3 : The reminder is the sum of all the digits taken 2 digits at a time. So, the reminder is 9 + 64 = 73.

So, the quotient is 9 and reminder is 73.

From the above table, 73 / 99 = 0.737373. So 964 / 99 = 9. 737373


Example 2 :
Find 995 / 99

Solution : Step 1 : Here 995 is the dividend and 99 is the divisor. In this example, divisor has 2 digit. So, set 2 digit from right as reminder.

Step 2 : The quotient is just the digit on the left. In our case, it is 9. So, the quotient is 9.

Step 3 : The reminder is the sum of all the digits taken 2 digits at a time. So, the reminder is 9 + 95 = 104. If the remainder is equal or more than 99(divisor), the difference is carry forward to the quotient just like in multiplication.

So, the quotient is 9 + 1 =10 and reminder is 104 - 99 = 5.

From the above table, 5 / 99 = 0.050505. So 498 / 99 = 10 .050505


Dividng a 4-digit number


When the dividend is a 4-digit number, the steps remains the same as, when the number is a 3-digit number. However, it is very important to remember about the carry-forward when the reminder when it is greater than 99. Let me explain considering a simple example.

Example 3 : Find 4168 / 99

Solution : Step 1 : Here 4168 is the dividend and 99 is the divisor. In this example, divisor has 2 digit. So, set 2 digit from right as reminder.

Step 2 : The quotient is just the digit on the left. In our case, it is 41. So, the quotient is 68.

Step 3 : The reminder is the sum of all the digits taken 2 digits at a time. So, the reminder is 41 + 68 = 109. Since 109 is greater than 99(divisor), the difference is carry forward to the quotient just like in multiplication.

So, the quotient is 41 + 1 = 42 and reminder is 109 - 99 = 10.

From the above table, 10 / 99 = 0.101010 So 4168 / 99 = 42.101010



Dividing a 5-digit or more


When the dividend is a number having 5 or more digits, there is a slight variation however.

Example 4 : Find 777745 / 99

Solution : Step 1 : Since we are dividing the number by 99(2 digit), set 2 digit from right as the remainder. In our case it is 45.

Step 2 : The quotient is the successive sum taking 2-digits at a time. So, the quotient was obtained by taking the successive sum taking 1-digit on the right at a time.

77 + 77 | 77

77 + 154

(77 + 1) + 54

So, the quotient after the carry-forward is 7854.

Step 3 : The reminder is the sum of all the digits taking 2-digits at a time.

i.e., 77 +77 + 45 = 199

Notice, that the reminder is greater than 99. If the remainder is equal or more than 99(divisor), the carry forward to the quotient is just like in multiplication.

So, the quotient is 7854 + 2 = 7856 and reminder is 199 - 99(2) = 1.

So, 777745 / 99 = 7856.0101


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