i need to know the answer for this prob not a hint on how to solve it?

Question

Consider all the whole numbers from zero to 1 billion (1,000,000,000). What is the sum of all digits needed to write down these numbers?

Answer 1

I'm interpreting this problem differently than the others who have posted before. You are considering the sum of the digits for each number, and adding together the sum of all the sums of the digits, for all numbers in the range 0 to 1 billion.

Well for all numbers 0-9, you would have 0 + 1 + 2 ... + 9, which is 1 * 45.

For all numbers 0-99, you have 10 * 45 for the digits in the 10s place, plus 10 * 45 for all the digits in the 1s place, which is 20 * 45.

For all numbers 0-999, you have 100*45 for the digits in the the 100s place, plus 100 * 45 for all the digits in the 10s place, plus 100 * 45 for all the digits in the 1s place, which is 300 * 45.

For all the numbers 0-9,999, it would be 4,000 * 45.

For all numbers 0-99,999, it would be 50,000 * 45.

And following the pattern, for all numbers 0-999,999,999, it would 900,000,000 * 45.

That calculates out as 40,500,000,000

But you have to add the sum of the digits of the number 1,000,000,000 to that. The sum of *those* digits is 1, so the answer would be 40,500,000,001.

Answer 2

Friedrich Gauss answered this problem as a grammar school student. I'm afraid you have to take his hint how to solve it. Let's take the problem that Gauss solved for his grammar school teacher, the sum of all digits from 1 to 100. First, 1 + 99 = 100. Next 2 + 98 = 100. So for numbers 1-49, you get 49 x 100 = 4900. Number 50 is alone, because it is unmatched by another number. So far, the total is 4950. If you exclude 0 and count 100, the answer is 5050.

For your problem, you have 1 + 999,999,999 = 1,000,000,000. Next, 2+ 999,999,998 = 1,000,000,000. You go on until only 500,000,000 is alone. You add that. Then you add the final 1,000,000,000.

Answer 3

I think what you are asking is what is the sum of all numbers from 1 to 1 billion.

If that is so, the sum of all numbers from 1 to n is:

n(n+1)/2

Going to be a BIG number!

on the other hand, if this is a trick question, the sum of all digits available to write any number is 1+2+3+4+...+10=55

Hope that this helps

:)

Answer 4

>>pls. coach me the suggestions... i'm no longer likely to do your homework for you, no longer to indicate for unfastened. yet i will a minimum of coach you the way you would be waiting to remedy them on your individual. a million. If n is the quantity, then its reciprocal is a million/n. So n + a million/n = 10/3. remedy this for n (hint: multiply the two facets by using n first). 2. If it grew to become into better by using x, then the dimensions grew to become into better to twenty-5+x and the width to 50+x. So the hot section is (25+x)(50+x). Set this equivalent to 4 hundred and remedy for x (hint: strengthen the expression and get it right into a quadratic equation). 3. If there are n human beings in the room, then each of them shakes palms with n-a million different individuals. So it would look there are n(n-a million). in spite of the fact that if, we are counting each handshake two times, in view that a single handshake is a handshake for 2 diverse human beings on the comparable time. So set n(n-a million)/2 equivalent to twenty-eight and remedy for n. 4. One practice's speed grew to become into s, and the different grew to become into s+10. After one hour, those might additionally be their distances from the station in kilometers. Use the Pythagorean theorem to locate the gap between the two trains (draw a diagram to work out why), set it equivalent to seventy one, and remedy for s. Then write s and s+10. 5. remember the element of a triangle is (a million/2)bh, the place b is the backside and h is the peak (or altitude). If the peak is h, then the backside right it somewhat is h-4. Plug those into the formula, set it equivalent to the given section, and remedy for h. Then use h to locate the backside length too. >>tnx and godbless i'm an atheist, yet thank you for the thought.

Answer 5

for every n-digit number, the digits involve to express them in written form is

9^n*[10^(n-1)]

and up till 999999, that is n from 1 to 6, just plug n in and sum them up. dont forget the 7 digits in a million.

9 +180 +2700 +36000 +450000 +5400000 +7
=5888896 digits

this is up to 1 million.

for 1 billion,

9 +180 +2700 +36000 +450000 +5400000 [phone] [phone] [phone] +10

=8888888899

Answer 6

this smoke screen question

all u need is the is 1+2+3....+9