Question

Find the number of all three-digit natural numbers,
which are divisible by 9.
(CBSE 2013)​

Answer 1

Answer:

Step-by-step explanation:

Three digit numbers start from 100 and end at 999.

Smallest three-digit natural number which is divisible by 9 is 108.

Now from 108, if you repeatedly add 9 with 108(until you reach 999), then the result will be a three-digit natural number divisible by 9.

That is first you get 108+ 9=117

Then 117+ 9 = 126

Then 126 + 9 = 135

……

until you reach 999.

Logic is that, as 108 is divisible by 9 then (108+9×n) will also be divisible by 9.

Where n is the number of times you add 9 with 108.

Now, question is …. maximum how many times we can add 9 with 108 this way?

At last, 108 + 9×n will be equal to 999(as 999 is the largest 3-digit number divisible by 9).

108+ 9×n = 999

=> 9×n = 891

=> n = 891/9 = 99.

So, maximum 99 times you can add 9 with 108.

Thus there are 99 three-digit natural number after 108 which are multiple of 9.

Therefore

Including 108 there are 99+1= 100 number of 3-digit numbers which are divisible by 9.

Answer is 100

Answer 2

Answer:

SUM OF ALL 3 DIGIT NUMBERS DIVISIBLE BY 8

About the topic "Sum of all 3 digit numbers divisible by 8"

"Sum of all 3 digit numbers divisible by 8" is a difficult problem having had by the students who study math to get prepared for competitive exams.

For some students, getting answer for the questions like "Find the sum of all 3 digit numbers divisible by 8" is never being easy and always it is a challenging one.

Once we know the concept and method of solving, solving the above problem will not be a challenging one.

To get the sum of 3 digit numbers divisible by 8, first we have to find the first and last 3 digit numbers divisible by 8.

First 3 digit number exactly divisible by 8

The smallest 3 digit number = 100

The first 3 digit number is also 100.

To find the first 3 digit number divisible by 8, we divide the very first 3 digit number 100 by 8.

100/8 = 12.5

We have decimal in the result of 100/8.

Clearly the first 3 digit number 100 is not exactly divisible by 8.

Let us divide the second 3 digit number 101 by 8.

101/8 = 12.625

We have decimal in the result of 101/8 also.

So, the second 3 digit number 101 is also not exactly divisible by 8

Here, students may have some questions on the above process.

They are,

Step-by-step explanation:

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