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.