If you write out all the numbers from 1 to 5000, how many times do you write 9?

Question

Can somebody please explain to me how you do this?? I don't really get how you do this question.

Answer 1

Think, how many times do you write 9 from 1-100?

Now, that should be the same number from 101-199...etc...up to 801-899

900-999 how many times??

Add up all the times together from 1-999 then multiply by 5 to get to 5,000.

Check your answer.

Answer 2

Simplest way i can figure this out is:

In the first 100 consecutive numbers (starting at 0), the number 9 appears 10 times in 9,19,29,39 etc and another 10 times in the 90 - 99 range. So in every one hundred numbers 9 appears 20 times.

Now in 1000 numbers the number 9 appears 20 * 10 ( as there are 10 lots of 100 consecutive numbers) so that is 200 9's in 1000. But there are more nines in the 900 - 999 range, 100 more in fact. So in every hundred there are 20 nines, in every thousand there are 300 nines. The number of nine's in 5000 can now be easily worked out.

300 * 5 = 1500

Answer 3

You can start by breaking up the problem:

From 1 to 100, there's one nine used for each of 9, 19, 29, 39, 49, 59, 69, 79,  and 89. That's nine 9's. From 90 through 98, there are nine more used. For 99, two 9's are used. That totals twenty 9's.

There will also be a total of twenty nines used for 101-200, 201-300, etc through 701-800. That gives you 20 times 8 intervals or 160 9's through 800.

The 801 through 900 interval has an extra 9 because of the value 900 at the end of it. That brings the total to 181 9's through 900.

The 901 through 1000 interval has the same twenty as the other intervals plus one each for the hundreds digit of each number. So from 901 through 999, there are an extra 99 9's. That makes 119 total 9's for this interval.

Adding the 119 from the 901-1000 interval to the previous 181 makes a total of 300 9's from 1-1000.

The 300 9's repeats for 5 intervals of 1000 which gives a total number of nines used of 1500.

Answer 4

answer is 1500.

Answer 5

uhm you count up to 5,000, and every time you write a number with 9 in it you tally until you get to 5,000