Kinds of number and significant digits.

 Kinds of Number 

There are two kinds of number, exact and approximate.

Approximate numbers

Approximate numbers are those that represent the number to a certain degree of accuracy.

Example; An approximate value of π is 3.1416 or if we wish to have a better approximation, it is 3.14169265. But we cannot write the exact value of π.

Exact numbers

The numbers which are accurately expressed are called exact numbers.

For example; 1,2,3…., 1/2,3/2,…. √2, π, e etc written in this manner.

Significant digits

The digits that are used to express a number are called significant digits or significant figures.

Example; The numbers 3.1416, 0.66667, 4.0687 contains five significant digits each. The number 0.00025 has however, only two significant digits viz 2 and 5 since zeroes serve only to fix the position of decimal points.

Similarly, the numbers 0.00145, 0.000145, 0.0000145 all have three significant digits.

Rule for finding significant digits

Rule 1: Every non zero digit is significant.

Example; 456 has 3 significant digits.

                 68.24 has 4 significant digits.

Rule 2: Zeroes between non zero digits are always significant.

Example; 5604 has 4 significant digits.

                 700.0879 has 7 significant digits.

Rule 3: Zeroes before non zero digits are not significant digits.

Example; 0.067 has two significant digits.

                 0.000008 has one significant digit.

                 098 has two significant digits.

Rule 4: Zeroes behind non-zero digits are sometimes significant.

Let us discuss it in detail.

A final zero or trailing zero in the decimal position only are significant.

Example; 0.00500 has three significant digits. 

0.03040 has four significant digits. 

Trailing zeroes in whole number are not significant.

Example; 200 has only one significant digit, while 25,000 has two significant digits.