## What is an Order of Magnitude?

### Introduction

Most of the time, we hear scientists use the word order of magnitude to describe the size of different objects. What does it mean if an object is described by order of magnitude? In order to understand the concept of order of magnitude completely, it is important to understand scientific notation.

## Scientific Notation

The scientific notation is a way of writing bigger and smaller numbers as the power of 10. For example 0.001 can be written as 1 × 10 ^ 3 which is a very small number. Similarly 100,000 can be written as 1 × 105 which is a bigger number.

Here one thing is to be noted while expressing the number in scientific notation. If the number is small we move the decimal point to the right side and to the left side if the number is large. The positive sign in the power of 10 indicates the larger number and the negative sign indicates the smaller number.

## What is the Order of Magnitude?

The concept of order of magnitude is based on scientific notation. It is a factor that gives us the idea how big or small a physical quantity is. The order of magnitude of a physical quantity is defined as the power of 10which is closest to the magnitude of that physical quantity.

For example, if we want to express a number N in the form of order of magnitude then there will be number x such that 0.5< n ≤ 5 so,

$$N\;=\;n\;×\;10^x$$

The number x is called the order of magnitude of N. If the value of x is 2 then we will say the number has two orders of magnitude. And 1 order of magnitude means the object is 10 times bigger.

Order of magnitude is used for describing roughly how big something is. It is also useful when talking about ting and microscopic numbers such as the diameter of an atom. For example a pineapple is 1 order of magnitude larger than a lemon. It means that the pineapple is 10 times larger.

## Why do we use Order of Magnitude?

The order of magnitude is used to make the size of measurements simple and understandable that helps in comparison of different measurements. It means that we can say that order of magnitude makes approximations and comparison between different objects easier.

We use order of magnitude to describe how the object is magnified. For example if we compare the size of the sun with the size of earth. The size of the sun would be much larger than the earth. So it is difficult to express it with simple mathematical notation. Therefore, we will use orders of magnitude for it. It will also help to identify how much the sun is bigger from earth.

## Example of Order of Magnitude

In many examples of larger and small numbers, the order of magnitude helps in writing in an understandable way. Some examples of such numbers are

• The age of Earth
• Circumference of Sun
• Diameter of Earth
• Distance measurement
• Approximations from different physical instruments.

## How is the Order of Magnitude Calculated?

The basic definition of scientific notation is used to calculate order of magnitude for any number. Let’s see in the following example how many numbers of magnitude there are.

### Order of magnitude calculation example no. 1

How many orders of magnitude are in 1,000,000 (one million)?

For the number 1,000,000, we will move the decimal point to the left and then stop just before the first digit of the number. Then the count of the number of digits after the movement of the decimal point to the left is the order of magnitude.

Since we moved it six times, there are six orders of magnitude of 1,000,000, meaning that you can multiply 10 six times and get 1,000,000. So writing the number in scientific notation,

$$1,000,000\;=\;1\;×\;10^6$$

### Order of magnitude calculation example no. 2

How many orders of magnitude are in 0.000001?

In this example, we will move the decimal to the right side and stop just before the first non-zero number. Now counting the digits that we move to the right side. The number of digits is 5. So the order of magnitude of 0.000001 is 5.

$$0.000001\;=\;1\;×\;10^{-5}$$

We will write the negative sign in the power of 10 because the number is much smaller.

## FAQ’s

### Can Order of Magnitude be Negative?

Yes, the order of magnitude can be negative. It is because of the smaller number such as 0.001. The order of magnitude of this number is 2 that is calculated by moving the decimal to the right side. In scientific notation, when the decimal is moved to the right side, the negative sign is placed in the power of 10. So the order of magnitude of 0.001 is -2.

### What is Meant by Order of Magnitude?

The order of magnitude means how big or small an object is. It gives the idea of comparison between different objects.

### What is a magnitude of 2?

The order of magnitude defines how much big or small an object is. If a quantity has magnitude of 2, it means that the number is 2 times larger than the order number.

### How many Orders of Magnitude is 1000?

Since the number 1000 is obtained by multiplying 10 three times, so the order of magnitude is 3.