​​Finding Digits of a Number

The smallest mathematical unit of the number system, i.e. the digits of a number, are the symbols that make up the numeral. For example, if there is a number 36, the digits of the number will be 3 and 6, i.e. the number has two digits. You can easily find the digits of a number by counting. For example, 145677 has 6 digits. The digits of any number are represented by 0, 1,2, 3, 4, 5, 6, 7, 8, 9 numerals. Thus, we can say there are 10 digits in arithmetic that, in different combinations, form numerals. We use these digit and number systems in our daily lives. 

Digits of a Number Importance

No doubt, digits are the basis of the number system. The number system is used in our daily lives, from shopping the groceries to tackling big targets for the company. Every field requires a digit and number system to work efficiently. Some of the digits of a number system importance are as follows:

• It helps us determine the costs, revenues, targets, profits and losses of the company.

• The knowledge of digits is necessary for performing all arithmetic operations such as addition, subtraction, multiplication, division and others.

• Understanding the place value of digits helps us in calculating and comparing numbers.

Finding the Number of Digits in a Square Root

A square of the number represents the multiplication of the number by itself. For example, the square of the number 9 will be 9×9, i.e. 81. On the other hand, the square root represents the number which is itself someone’s square. For example,  √81 will be equal to 9, which means 81 is the square of 9. In other words, we can say that the square root of any number represents the value of 1/2th of that number.

√n2 = √ (n × n) = n

n= positive integer.

For finding the number of digits in the square root, we must be aware of whether the number is odd (not divisible by 2) or even (divisible by 2). A number having 0, 2, 4, 6, 8 at the endings is always considered even and is definitely divisible by 2.

On counting, if you find the total numbers of digits even, then the formula used for the calculation of digits in the square root shall be N=n/2.

n= Number of digits

However, on counting, if you found the total number of digits odd, then the formula used for the calculation of digits in the square root shall be N=n+1/2

Example:

Case 1: If the number of digits is even,

The number of digits in 81 is 2 so, n=2

As we know, the number of digits is even. Therefore, the number of digits in the square root shall be:

N=n/2

N= 2/2

The number of digits in the square root of the number 81 shall be=1, i.e. 9.

Case 2: If the number of digits is odd,

The number of digits in 196 is 3 so, n=3

As we know, the number of digits is odd. Therefore, the number of digits in the square root shall be:

N=n+1/2

N= 4/2

The number of digits in the square root of the number 196 shall be= 2 i.e. 14.

Solved Questions on Finding Digits of a Number

Q 1- On interchanging the digits of a two-digit number, we get a number 18 greater than the original number. On adding the digits of the original number, we get 8. Calculate the original number and twice the original number?

Solution:

Assume the unit digit and ten-digit as x and y respectively.

According to the question,

x + y= 8 and x – y = 18 ÷ 9 = 2

Therefore,

x = (8 + 2) ÷ 2

= 5 and

y = 5 – 2

= 3

Therefore, the original number will be 35.

And twice of the original number= 35× 2

=70

Q 2- Determine the total 3 digit numbers that are completely divisible by 6.

Solution:

The three-digit numbers start from 100 up to 999. Therefore the total number of 3 digit numbers is 900.

The smallest 3 digit-number divisible by 6 will be 102 (6 × 17), whereas the largest 3 digit number divisible by 6 shall be 996 (6 × 166).

Moreover, the total 3 digit-numbers that are completely divisible by 6 will be= 166 – 17 + 1

= 150.

Q 3- All the natural numbers up to 100 are multiplied together. Calculate the total number of zeroes obtained after the product of all natural numbers up to 100.

Solution:

The total numbers, i.e. the ‘n’, will be= 100 (natural numbers start from 1)

The number of zeros at the end of the product of all natural numbers up to 100 will be:

= (100 ÷ 5) + (100 ÷ 5^2)

= 20 + 4

= 24

Conclusion

Digits of a number are the smallest value or the sole symbols used to represent numbers. If there is a number such as 8112, the digits of this number will be 4. The digits or the basics of the number system and the number system is the base of arithmetic. Not only in mathematics, but the number system is also important in every field related to maths. The square root of any number represents the value of 1/2th of that number. For example, √64 will be equal to 8, which means 64 is the square of 8.