# what is the difference between significant figures and standard form and please give some examples.

Posted on

Numbers can be written in different forms. Scientific notation is used to make writing large or small numbers easier to understand.

In scientific notation all numbers are written in the form `c "x" 10^n` where `0<=c<10` (note the strict inequality for c<10), c is a real number and n is an integer.

For example 117,000(standard) would be written `1.17"x"10^5` (scientific notation)

.000117 would be written as `1.17"x"10^(-5)`

Suppose you were asked to find the area of a rectangular plot that was 2200m by 6300m. You could take 2000x6300=13860000m. But it is easier to see `(2.2"x"10^3)(6.3"x"10^3)=13.86"x"10^6=1.386"x"10^7`

A number like 1,000,000,000,000 is beyond the imagination, and we really do not have a good grasp of such large numbers. But it is easy to compare them in scientific notation: `1"x"10^12`

** Engineering notation is also used frequently -- it is basically scientific notation except for values between .001 and 1000 you would use standard notation. So a man weighs 200lbs but a car weighs `2.2"x"10^3` lbs.**

-----------------------------------------------------------------

Significant digits come into play when you do applications -- especially in physics or engineering. If all of the measurements are to the nearest 100, but in the course of doing calculations we get 110,719 then the correct answer is 110,700 or `1.107"x"10^5` .

If there are only three significant digits in any of the data, then the correct answer to the above problem is `1.11"x"10^5`