How Many Whole Numbers Between 100 and 500 contain the digit 2?

Question

This Question is not very difficult but i just wanna know an easy way to do it, instead of counting.

Answer 1

There are exactly 157 numbers with a 2 in them in that range, here's how I broke it down:

Numbers 200-299: 100

Numbers between 100-199 & 300-500 ending in 2: 30

Numbers between 100-199 & 300-500 with a 2 as the tens column digit and excluding those ending in 2: 27

100 + 30 + 27 = 157

Answer 2

Let's break this down and save you some counting....OK?

There are ten main numbers in each series of 100...i.e (102,112,122,132,142,
152,162,172,182,192),
but we have to include all of those in the series 120 - 129 of which there are nine numbers but as already pointed out above 122 has already been counted so you take 10 + 9 per hundred = 19.

Do the same for 300, and 400... again 19 each
3*19 = 57 (Remember this number)

The 200 series contains a 2 in each from 200 - 299 therefore another 100 numbers containing a digit 2.

Add 100 + 57 (the number from above) and you have 157 numbers between 100 and 500 that contain the digit 2

Hope this helps

Answer 3

Here's the easiest way. Count how many numbers do *not* contain 2, and subtract.

There are 3 slots. The first one can be 1, 2, 3, 4. The second and third can be 0-9 (and then add 1 for 500).

So, there are 3*9*9 + 1 = 244 numbers in this range with no 2's in them, and 401 numbers altogether in the range, so 401 - 244 = 157 numbers containing the digit 2.

Answer 4

The easiest way (the easiest that comes to mind at the moment,anyway) is this.

1. Start with numbers 01 - 99. Number 2 appears at least once in every decade (2, 12, 22, 32, etc), and, since you have 10 decades, there are at least 10 numbers with digit 2 in them. Now, observe numbers 20 - 29. There are 10 numbers which have digit 2 in them, but, since we have already counted 22, we only consider 9 of these 10 numbers. So, it's 19 numbers in total.

2. Observe numbers 100 - 500, but exclude those that are 200 - 299. If you apply what we've said in 1. you will get this:
- 100 - 199 contain 19 numbers with digit 2
- 300 - 399 contain 19 numbers with digit 2
- 400 - 499 contain 19 numbers with digit 2

So, in total, there are 3 * 19 = 57 numbers with digit 2 in them (counting only those that are not within 200 - 299 range.

3. 200 - 299 has 100 numbers with digit 2 in them, so, by adding what we have from 2. we get 157 numbers with digit 2 in them.

Answer 5

For every 100, between 100 and 500, there are:
10 in the 20's and 9 in the others - i.e. a total of 19.
Therefore in 400 numbers there are - 76 2's.
There are an additional 100 2's in the 200's.
Therefore the total number of 2's is 176.

Answer 6

Prime Numbers 100-200

Answer 7

Sorry, my original answer was wrong.

I thought there were 133, but when I check my work, again,
I found I was wrong. I was not counting number like 121, 122, only 120

--- how to get the wrong answer ---

102:10:492 there are 49-10+1=40 (number like **2)
120:100:420 there are 4-1+1=4 (number like *2*)
200:299 there are 99-00+1=100 (number like 2**)
this give 144 but you counted
2*2 twice and the number 222 three times.
202:10:292 there are 9-0+1 = 10 of these including 222
222 there is only one 1
therefore there is
144-10-1=133

-----
instead of me counting I let the computer do it.

n=0;
for i=100:500;
if findstr('2',num2str(i))>0,
n=n+1;
end;
end;
n

Answer 8

100 >> 199 ..... 19 2s
200 >> 300 ..... 100 2s
300 >> 400 ..... 19 2s
400 >> 500 ..... 19 2s

Then total 2s = 157 2s

For every 100 numbers you get 19 2s, and between 200 and 300 you get 100 2s...

If you have Excel you can try putting this formula in

Put the initial number in this case 100 in cell A1, put the final number in this case 500 in cell B1, and then put this formula in cell C1 "IF(B1=>300,((((B1-A1)/100)-1)*19)+100,if(B1=200,((((B1-A1)/100)-1)*19)+1,((((B1-A1)/100)-1)*19)))"........

That for Excel will take care of any list of numbers with extremes ending in 00 like 100, 200, 300, etc....

Answer 9

100-199 has 19 whole numbers containing 2
200-299 has 100 whole numbers containing 2
300-399 has 19 whole numbers containing 2
400-500 has 19 whole numbers containing 2

therefore.....100+19+19+19 = 157

Answer 10

40