Order of magnitude

[Disclaimer: I just wanted to share some things which I am learning.Kindly confirm those from the textbooks.]

Hello friends,

Today we will learn about order of magnitude. In measurement this chapter is very important. First, let us see about what is order of magnitude. Let us find out.

3.1 – Introduction

So friends, this is our third chapter! You had learnt about units & dimensions. Now we will learn about order of magnitude. You know that there are very large quantities & very small quantities. For example, the speed of light in air is 300000000. This is very large. But on the other hand, the magnitude of the charge on an electron is 0.00000000000000000016 coulomb. This is too small.

This is very boring to write these zeros. So we can write these numbers in a shorter form. How to write it? In 8^th standard you had learnt about that method. But now we will revise it today. Let’s revise the method of power of ten.

3.2 – Method of power of ten

Consider the number 460000000000. In this number it is very inconvenient to write these zeros. Here we will use the method of power of ten. For making this number short we have to use the following steps.

STEP 1

In step 1, first count the number of zeros. So you will find that there are 10 zeros. Now add 1 in that number of zeros. This is equal to 11.

Number of zeros + 1 = 10 + 1 = 11

STEP 2

In step 2, remove all zeros in that number & write down the remaining number. So, in this case, when we remove all the zeros in that number then the number will be 46. Now, we will write down the number 46.

46

STEP 3

Now in this step, we have to dissect the number 46 in digits & we will add a decimal point after the first digit. So the final number will be 4.6. Write down the number 4.6 as follows.

4.6

STEP 4

In this step, we will add a multiplication symbol after 4.6 & then we will write the number 10. Then, in step 1 our final answer was 11. So we will write the power of 10 as 11. So we will write it as 10¹¹. So write down our final answer as given below.

4.6 x 10¹¹.

In this case we had avoided the repetition of the zeros. In similar manner let us consider the digit 0.000000000019. For making this number short we have to use the following steps.

STEP 1

In step 1, first count the number of zeros which are after the decimal points. So you will find that there are 10 zeros. Now add 1 in that number of zeros. This is equal to 11.

Number of zeros + 1 = 10 + 1 = 11

STEP 2

In step 2, remove all zeros & decimal points in that number & write down the remaining number. So, in this case, when we remove all the zeros & a decimal point in that number then the number will be 19. Now, we will write down the number 19.

19

STEP 3

Now in this step, we have to dissect the number 19 in digits & we will add a decimal point after the first digit. So the final number will be 1.9. Write down the number 1.9 as follows.

1.9

STEP 4

In this step, we will add a multiplication symbol after 1.9 & then we will write the number 10. Then, in step 1 our final answer was 11. So we will write the power of 10 as 11 & we will add negative symbol before 11. So we will write it as 10^-11. So write down our final answer as given below.

1.9 x 10^-11

So you had revised this clearly. Your basic concepts are cleared. So let us see about order of magnitude.

3.3 – Order of magnitude

You had learnt about the method of the power of 10. But now we will learn about what is order of magnitude. In the above examples the positive indices of 10 represent large magnitudes while the negative indices represent small magnitudes. So we can write the speed of light in convenient form as 3 x 10⁸ m/s while we can write the charge on an electron as 1.6 x 10^-19 coulomb.

How to find the order of magnitude? The order of magnitude of a number is defined as the power of ten nearest to that number. So the order of magnitude of 432 is 10². This is because this number is closer to 10². Means the number 100 is closer to 1000. So the order of magnitude of 432 is 10². On the other hand, the magnitude of the number 0.00325 is 10^-3.

It was very easy, isn’t it? Now I think you had learnt this chapter clearly. Thank you for watching my blog.

3.4 – Thank you

So friends thank you for watching my website. Best of luck for your exams… See you next time.

Your friend,

Aditya P