Question

In the product of 200 and 25, which digit is in the hundred’s place?
A) 0
B) 5
C) 10
D) None of these

Answer 1

Hint:
When an even number is multiplied by a number divisible by 5 (which are the numbers ending with a 0 or a 5), the digit at the unit's place of the product is 0. The hundred’s place of number is found at the third place from the left.

Complete step by step solution:
It is a very well-known fact that when an even number is multiplied by a number divisible by 5 (which are the numbers ending with a 0 or a 5), the digit at unit’s place of the product is 0.
This is because when two numbers are multiplied, out of which at least one is even, the number is even. And since we multiplied a number which is divisible by 5, we will get a number which is even and divisible by 5, and this kind of number is always divisible by 10. And we know that a number divisible by 10 always ends with a 0.
Now, for calculating the answer to the given question, we need to determine what digit is in the hundred’s place. The first number from the left of a number is the unit’s place, then the next number after this number (that is, the second number) is the ten’s place, then the next number after this number (that is, the third number) is the hundred’s place, and so on and so forth. So, we need to find what number is at the third position.
The number being multiplied is 200. Clearly, 200 is a three-digit number which has the numbers at the first and second position (that is, the number at the ten’s and unit’s place) equal to 0. So, we have to find what multiplying 2 with 25 gives us.
Now, 2 is even and 25 is divisible by 5. So, from the above explained rule, the last digit of the product will be 0. Hence, the third number (hundred’s place) of the product of 200 and 25 is 0.

Hence, the correct option is A.

Note:
So, we saw from this question that to solve the whole thing without actual multiplication the only thing that is needed to know is that when an even number and a number divisible by 5 are multiplied, we get a number which ends with a 0. And when an odd number is there, then the product ends with a 5 if the number divisible by 5 ends with 5, and 0 if it ends with a 0.