Question

If Whitney wrote the decimal representations for the first 300 positive integer multiples of 5 and did not write any other numbers, how many times would she have written the digit 5

Answer 1

201 times

Explanation:

Since it's the first 300 positive integer multiples of 5, then the last integer will be: 300 × 5 = 1500

While the first is 5.

The sequence is like this;

5, 10, 15, 20, 25, 30, 35, .. 1500

Since for every 2 integers that are multiples of 5, 1 will include the digit 5, then it means that, number of times the unit place will have 5 is; 300/5 = 150 times

Now, between 5 and 100, the only value that has 5 in it's tense place is 50 & 55.

So for every 100 numbers, we have 2 times to write 5 in the tens place. Thus, for 1500 numbers, we will write 5 in the tens place: 1500/100 × 2 = 30 times

Now, for the hundreds place, from 500 and 600, we have 21 multiples of 5 inclusive of 500 and 600 but since we want the one that has 5 in the hundreds place, then it is 20 as they all start with 5 excluding 600.

Also, from 1000 to 1500, the only number that has 5 in its hundreds place is 1500.

Thus,total times 5 is written in the hundreds place = 21 times

Total number of times 5 is written = 150 + 30 + 21 = 201 times