Order of Magnitude: How to calculate it?

Introduction

The order of magnitude is essential in mathematics and other fields of science such as physics, chemistry, biology, etc. It is used when we are dealing with very small or large quantities. In this article, you will learn more about the order of magnitude and determine how it helps in simply writing very large and small numbers. 

Order of magnitude is a way of comparing the most significant and smallest values using scientific notation. To understand the order of magnitude, we should know what scientific notation is. So, before understanding the order of magnitude, let’s understand scientific notation first. 

What is Scientific Notation?

Scientific notation is a way of writing small and big numbers in a standard form. It is also known as the scientific form, common index form, or standard form. It is widely used by scientists, mathematicians, and engineers because it can simplify certain numeric operations. 

A number’s scientific notation is written using some power of ten. For example, to write 0.00056 in scientific notation, we first move the decimal to the right-hand side until the last non-zero digit. Count the number of digits you moved till the final digit and write it as the power of 10, such as;

5.6 × 104.

If you are using an online scientific notation calculator, it will take input from you and instantly convert into scientific notation form.

What is the order of magnitude?

 The order of magnitude is a way of writing very small and large numbers. Scientific notation is used to find the order of magnitude of a quantity. It gives the idea of how big a physical quantity is from another one. A number N can be written as the order or magnitude such that there exists a number n as 0.5<n<5. Therefore, 

N=n × 10x

The term order of magnitude is used to describe the approximate size of something. It is also useful when discussing tiny and microscopic numbers, such as the diameter of an atom. It is used to make the size of measurements simple and understandable which is beneficial for comparing two or more physical quantities. 

For example, the temperature at the core of the sun is about 15,600,000 Kelvins. By using order of magnitude, we can write it as;

15,600,000 Kelvins=1.56 × 10

How is the order of magnitude calculated?

The order of magnitude is easily calculated by writing the given value in standard index form. You can use the following steps to find the order of magnitude. 

  1. To write the number in scientific notation by moving the decimal.
  2. If there are leading zeros, move the decimal to the right side.
  3. If there are trailing zeros, move the decimal to the left side. 
  4. Place the decimal just after the last non-zero digit by using the range 0.5<n<5.
  5. Now, count the number of digits that you skipped after moving a decimal point. 
  6. Write the number as the power of 10. Such as; N=n × 10x, the power of 10 is the order of magnitude. 

You can also use an order of magnitude calculator to write your number in this form.

Why do we use order of magnitude?

The order of magnitude is an important concept in approximately all fields of science. It helps to make the size of measurements simple and understandable so that we can easily compare one or more quantities together. We can easily approximate how much a number is bigger or smaller than the older one by using order of magnitude.

We use order of magnitude to describe how magnified an object is. Consider the size of the sun in comparison to the size of the earth. The sun is much larger than the Earth. As a result, expressing it using simple mathematical notation is difficult. As a result, we’ll use orders of magnitude to describe it. It will also help determine how much larger the sun is than Earth.

Conclusion:

The order of magnitude is an important concept that gives us the idea of how much a quantity is magnified. It makes the size of measurement simple and easier so that we can compare and calculate the size of two or more measurements. According to the above discussion, we can conclude that the order of magnitude uses scientific notation to write a physical quantity in a simple form. And the power of ten tells how one quantity is big or small from the other one. 

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