Question

How to find number of digits in mathematical expression?

Answer 1

⊕ANSWER⊕

• Let's say we have a three digit number abc.

• We can also write the number as a*100+b*10+c. So highest power of 10 present in the number is 2.

• And this is true for all three digit numbes as we have taken arbitrary values.  

• The number is of course in decimal system and any three digit number in decimal system will fall in between 100 and 1000.

• Logarithm of these are 2 and 3. (In base 10).

• So to calculate the number of digits in any number we can find the value of logarithm of that number and that will define the highest power of 10 present in the number.

• Like for the number 123, log(123)=2.0899, which implies that the number is greater than 100 but less than 1000. So it's a three digit number.  

• So number of digits in any number A is equal to Ceiling (log(A)).

• Where Ceiling is a mathematical function called Lowest integer function.  

• For any real number, the function is defined as the lowest integer but not lower than the real number.

• Like for 2.3, the value is 3.  

• So, to find the number of digits in n!

• we can use this formula.  

Number of digits in n!  

= Ceiling (log(n!))

= Ceiling (log( 1*2*3*........*(n-1)*n))

= Ceiling [log(1)+log(2)+....+log(n)]

• Now this formula can be applied to find the number of digits in a number in other bases also.

• For base n, we have to apply log base n instead of log base 10.

Answer 2

Answer:

Step-by-step explanation:

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