How many zeroes are there in the number which is made with integers from 1 to 1000 written on paper?
How many zeroes are there in the number which is made with integers from 1 to 1000 written on paper?
There are total 9 numbers between 1 to 99 which have only one zero are :
10,20,30,40,50,60,70,80,90
Therefore, total one zero numbers between 1 and 999( x0 format) are 9*10= 90 zeros.
And zeros which come in between 3 digit numbers are: eg: 101,102,103….109
Therefore, total one zero numbers between 1 and 999(x0x format) are 9*9= 81 zeros.
Now, 2 zero numbers in between 1 and 999 are:
100,200….900
So , No. Of zeros (x00 format)= 2*9 = 18
And 3 zeros of 1000 .
Therefore, total zero's are : 3+18+81+90 = 192.
If we write down the numbers from 1 to 10, we need to use 11 digits. If we write down the numbers from 1 to 100, we need to use 192 digits: one each for the number from 1 to 9, two each for each of the ninety numbers from 10 to 99, and three for the number 100. How many of these digits are zeros? The digit zero appears only in the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Thus, there are 11 zeros among the digits. This is the same as the number of digits in writing the numbers from 1 to 10. Now let us look at the numbers from 1 to 1000. To write all these numbers down, we need to use 9 + 180 + 2700 + 4 = 2893 digits to accommodate the 9 single-digit numbers, the 90 double-digit numbers, the 900 triple-digit numbers and the number 1000. How may zeros did we need? There are 9 numbers of the form d0, 9 numbers of the form d00 (each with two zeros), 81 numbers of the form d0k, 81 numbers of the form dk0, where d and k are one of the nine nonzero digits, and the number 1000. The number of zeros we need is 9 + 18 + 81 + 81 + 3 = 192.
There are total 9 numbers between 1 to 99 which have only one zero are :
10,20,30,40,50,60,70,80,90
Therefore, total one zero numbers between 1 and 999( x0 format) are 9*10= 90 zeros.
And zeros which come in between 3 digit numbers are: eg: 101,102,103….109
Therefore, total one zero numbers between 1 and 999(x0x format) are 9*9= 81 zeros.
Now, 2 zero numbers in between 1 and 999 are:
100,200….900
So , No. Of zeros (x00 format)= 2*9 = 18
And 3 zeros of 1000 .
Therefore, total zero's are : 3+18+81+90 = 192.
If we write down the numbers from 1 to 10, we need to use 11 digits. If we write down the numbers from 1 to 100, we need to use 192 digits: one each for the number from 1 to 9, two each for each of the ninety numbers from 10 to 99, and three for the number 100. How many of these digits are zeros? The digit zero appears only in the numbers 10, 20, 30, 40, 50, 60, 70, 80, 90, 100. Thus, there are 11 zeros among the digits. This is the same as the number of digits in writing the numbers from 1 to 10. Now let us look at the numbers from 1 to 1000. To write all these numbers down, we need to use 9 + 180 + 2700 + 4 = 2893 digits to accommodate the 9 single-digit numbers, the 90 double-digit numbers, the 900 triple-digit numbers and the number 1000. How may zeros did we need? There are 9 numbers of the form d0, 9 numbers of the form d00 (each with two zeros), 81 numbers of the form d0k, 81 numbers of the form dk0, where d and k are one of the nine nonzero digits, and the number 1000. The number of zeros we need is 9 + 18 + 81 + 81 + 3 = 192.
