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.

How to perform mutiplication and division?

Division and multiplication is often encountered in physics and it is very important that you know how to give the answer in the appropriate form.

Let us have a look at how division and multiplication is performed.

Multiplication

Let us see an example of a multiplication and see how to give the answer in the appropriate form.

23.2 * 3.1 = 71.92 = 72

Can you guess why the answer is 72?

Firstly you have to look at the number of significant figures in the two number used.

23.2    3 significant figures

3.1      2 significant figures

One of the numbers (3.1) has the smallest number of significant figures (2) as a result the answer must be given to 2 significant figures. Hence the answer is given as 72.

Let us have a look at a second example.

22.34 * 123 = 2747.82 = 2750

123 has 3 significant figures and 22.34 has 4 significant figures so the answer is given to 3 significant figures.

Have you guessed the law yet? If yes write it down. If not keep thinking. We will see it at the end of the post.

Division

In a way division is somewhat related to multiplication. Let us have a look at an example and see how the answer is given.

14.2 / 2.333 = 6.08658 = 6.09

As you can see it is similar to multiplication. The two number used has 3 and 4 significant figures respectively. And as a result the answer is given to 3 significant figures.

Let us have a look at a second example.

1.33 / 3.0 = 0.44333

Can you guess how to write the answer in the correct form?

Yes you have guessed right. It is 0.44. Since the two numbers used are at 3 and 2 significant figures respectively, then the answer is given to 2 significant figures.

So have you guessed the rule that govern the multiplication and division? Here it is!!

When a multiplication or a division is performed, the answer is given to the same number of significant figures as the number used with the smallest number of significant figures.



It is now time to do some exercises.

1. 1.2 * 343


2. 2.3 / 3.55


3. 3.4 * 0.2222


4. 3.555 * 434 / 0.32

I will give the correct answer after a few of you have submitted your answers in the comment section.

See you later my students.

How to perform addition and subtraction in physics

In physics we often encounter calculations where you have to add two numbers together or we had to subtract one number from another. This is particularly important when data from practical sessions are processed even though additions and subtractions are often met in the syllabus.

However, as I have said in the introduction, the answer must be given to a certain number of decimal place. If you cannot say what the number of decimal place a number has, please refer to this post on decimal place.



Addition

Now let us see an example on how to add two numbers.

4.43

7.6    +

_____

12.03

____

12.0     Final answer.

So how do you give the answer to the appropriate number of decimal places? Add the two numbers and you get the answer 12.03. But this is not the final answer to the addition.

Before you write the final answer, look at the two numbers and determine the number of decimal places for each.

4.43    2 decimal places

7.6      1 decimal place

Now what is the smallest number of decimal places in the two numbers?

7.6 has 1 decimal place so the answer must have 1 decimal place. So the final answer is 12.0 with 1 decimal place.

Let us have a look at a second example.

67.54             2 decimal places

45.345            3 decimal places

______

112.885

112.89            Final answer2  decimal places

This is not the final answer. The two numbers used has 2 and 3 decimal places. So the final answer must be given to 2 decimal places. So the final answer is 112.89

Easy isn’t it.



Subtraction

Now we are going to see how subtraction is done. Here an example.

34.9

32.09  -

____

2.81

2.8      Final answer

So have you guessed how the answer is obtained?

The first number has 1 decimal place and the second number has 2 decimal places. As a result the answer must have 1 decimal place.

Let us have a look at a second example.

123.7             1 decimal place

3.433         3 decimal places

______

120.267

120.3             Final answer

1 decimal place

Have you got it? Let me summarise this with a rule.

When an addition or a subtraction is performed the answer is given to the same number of decimal places as the number used that has the smallest number of decimal places.

It is very important that you remember this law.

It is now time to do some exercises.

1. 12.45 + 34.555


2. 2.3 + 23.4445


3. 3.444 - 545


4. 34.3 – 34.111


5. 44.009 – 23.2

Do the following exercises and leave the answer in the comment section. I will give the correct answer later on when a few of you have submitted your answers.