How to perform calculation involving lg and ln in physics?

The physics students are often faced with calculations involving logarithm either to base 10 or the natural logarithm. Just like addition, subtraction, multiplication and division, the answer to a calculation involving either lg or ln has to be given in a certain form.

Let us have a look at an example and then later on we are going to see the law.

lg 12.3 = 1.0899

Now is 1.0899 the correct answer?

Let us see how the answer should have been written and after that we will discuss the reasoning behind.

lg 12.3 = 1.0899 = 1.090

Can you guess the reasoning behind? The number being used has 3 significant figures and as a result the answer is given to 3 decimal places.

Let us have a look at a second example.

ln 1.98 = 0.98503 = 0.985

Since the number used has three significant figures then the answer is given to three decimal places.

Did you get it?

The rule when calculating with lg and ln is simply

The answer to a calculation involving lg and ln is given to a certain number of decimal places equal to the number of significant figures of the number used.



Now some questions for you.

1. lg 0.67


2. ln 6.7


3. lg 122


4. ln 6.777

Here you go my students. I will give you the answers to these questions later on.

Good luck.