# How many times will the 5 digit be used in numbering the pages of a 145-page book?

###### Wiki User

###### 2007-07-13 12:20:49

Assume that the pages are numbered 1-145 in order and we don't

have any other page numbering system.

In every ten pages the digit 5 will appear in the units column

once,

e.g. 5, 15, 25, 35, 45 etc.

That makes 15 fives.

In the 50's the digit 5 will also appear in the tens column

e.g. 50,51,52,53,54,55,56,57,58,59

That makes another 10 fives.

Don't worry about page 55, remember we counted the unit's digit 5

first then the ten's digit 5.

The book is too short to have digit 5 in the hundreds column.

So the digit 5 appears 25 times in the numbering of a 145-page

book. == Answer

== From 1 to 145, we have 9 one-digit numbers and 100 two-digit

numbers and 46 three-digit numbers

In one-digit numbers we have only **one chance** to have

5.

In two-digit numbers we can have 5 in the units place, in the tens

place or the both.

If we have 5 in the units place, then we can fill up the tens place

by the numbers from 1 to 9. So, we get **9 chances**.

If we have 5 in the hundreds place, then we can fill up the units

place by the numbers from 0 to 9. So, we get **10**

**chances**.

In three digit numbers, we can’t have 5 in hundreds place and tens

place because we have 145 pages in all. So, we can have 5 in

units-place only.

The hundreds place cannot be filled with any other number except

1.

So, we can fill the tens place by the numbers from 0 to 4 only. So,

we get **5 chances**.

In total, 25 times we come across 5. Source:

www.icoachmath.com