# Thread: Max Digits

1. ## Max Digits

Hi,
I am writing a C program that will allow me to determine the maximum number of digits that a value can have to be within the range 0..m.

for example:

if m=23
max number of digits =1
Actual range 0..9

if m=379
max number of digits =2
Actual range 0..99

if m=453638923
max number of digits =8
Actual range 0..99999999

where 9 is a digit not a value...

firstly I dont want code but could someone explain the above theory as I just dont get it....

2. log10(23) = 1.xxx
log10(379) = 2.xxx

3. I dont understand. Isn't the value 20 within the range of 0...23? 20 has 2 digits.

What you need to do to find out the max digits is to find the number of digits your 'm' has. I really dont know how to explain theory, but I can give you an example...

12345 / 10 = 1234.5
12345 / 100 = 123.45
12345 / 1000 = 12.345
.
.
.

remember that if both values are ints, then the fractional portion of the values will get truncated (cut off)

4. Salem made use of the logarithm function, it is in some way the inverse of the power function. Example:

10^2 = 100
log10 (100) = 2

Note that the base is 10, that's why it goes OK. For numbers with base 10, the total number of digits can be calculated as:

nr_of_digits = (int) log10 (N) + 1

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