definition of rounding off and approximation

Rounding off and approximation are very nearly the same thing. Rounding off usually means displaying a number in a lower precision (usually to a specified precision in the number of digits after the decimal) than is its real value. For instance the value of π (pi), which is an irrational number has infinite number of digits after the decimal point and can be displayed up to any precision desired. The first 75 digits of pi are 3.141592653589793238462643383279502884197169399375105820974944592307816406286. If a question specifies displaying pi rounded to a precision of 5 digits after the decimal, you would write the answer as 3.14159. The convention while rounding off is to add 1 to the last digit of precision if the number that comes after that digit is greater than 4 and leave the number as is if the next digit is less than 5. For instance pi rounded off to 4 digits will be 3.1416 because the 4th digit is 5 and the number that comes after the fourth digit is 9 which is greater than 4. If the specification is to display rounded off to 8 digits it will be 3.14159265. Here we copied the first 8 digits without changing the last digit 5 because the next digit is 3 which is less than 5.