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.

What is a physical quantity?

Physical quantities

A physical quantity is a property of an object that can be measured with a measuring instrument.For example length, width, time, weight, etc.

It is important for you to be able to say which instrument is used to measure which physical quantity.The table below shows a few examples of physical quantities and the instruments used to measure them.

Physical quantity Instrument

Length                                                        Metre rule

Temperature                                            Thermometer

Time                                                             Stopwatch

Volume                                                       Measuring cylinder

Of course as we go through the different chapters we will be able to introduce more physical quantities and their measuring instruments.

Basic and derived quantities

Quantities can be divided into two types :

1. Base quantities

2. Derived quantities

Basic quantities

Basic quantities are the fundamental quantities that are not related to each other and that are use to derive all other quantities.

There are seven basic quantities. They are

1.  length

2.  time

3. mass

4. Thermodynamic temperature

5. electric current

6. amount of substance

7. luminous intensity

Derived quantities

Derived quantities are just quantities that are derived from one or more basic quantities.

For example area is a derived quantity because it is derived from the basic quantity length.

Area = length * length

Volume is a derived quantities because it is derived from the basic quantity length.

volume = length * length * length

density is a derived quantity because it is derived from length and mass, two basic quantities.

density = mass/(length * length * length)

As you can see all other quantities apart from the 7 basic quantities are derived from the seven basic quantities and it can easily be shown as in the example above.

Can you show what are the basic quantities that are used to derive the following derived quantities?

a) force

b)  kinetic energy

c) power

d) pressure

I would give the answer after a few of you would have give your answers.

Good luck and see you next time.