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.
- 1.2 * 343
- 2.3 / 3.55
- 3.4 * 0.2222
- 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.
These are very important in calculating in uncertainties in physics. Could you tell me about some reference books.
ReplyDeleteIn fact there is actually no books where this is shown in great detail. Hence saw the need to collect all the information and to show it on this blog. If you read carefully in text books all of them give the answers according to the following rules but they dont say it explicitly.
ReplyDeleteI would suggest you use this blog as the reference