A girl wrote all the numbers from 100 to 200. Then she started counting the number of one's that has been used while writing all these numbers. What is the number that she got?
Answers
From 100 to 200 there are 101 numbers.
There are 100 1's in the hundred place.
10 1's in tens place10 1's in unit place.
Thus the answer is 100+10+10= 120.
So , the answer is 120
Answer:
From 100 to 200, '1' appears 120 times.
Step-by-step explanation:
The numbers are: 100, 101, 102, . . . . . . . . . , 199, 200
Therefore every number starting from 100 to 199 will have a 1 in the hundreds place = 100 times
Therefore, number of 1's in hundreds place = 100 --(i)
Now we will calculate the 1's that appear in the tens place
These numbers are 110, 111, . . . . . . . . . , 119
Therefore every number starting from 110 to 119 will have a 1 in the tens place = 10 times
Therefore, number of 1's in tens place = 10 --(ii)
Now we will calculate the 1's that appear in the units place
These numbers are 101, 111, 121, . . . . . . . . . , 191
Therefore for these numbers will have a 1 in the units place = 10 times
Therefore, number of 1's in units place = 10 --(iii)
Therefore, to find the total number of 1's that appear between 100 to 200 , we add equation (i) , (ii) and (iii)
=> 100 + 10 + 10
= 120
Therefore from 100 to 200, '1' appears 120 times.