Difference between Scientific Notation and the Order of Magnitude
Introduction
Measurement is the basis of science. It gives the idea of comparison between the sizes of different objects. We use scientific notation to express any measurement in a simple form and order of magnitude to find how magnified an object is. Both are excellent concepts for approximation of measurement. In this article, we will discuss more about them along with their differences.
What is Scientific Notation?
It is a way of writing very small or large numbers in the simplest form. The main purpose of writing the numbers in the simplest form is to compare them to find nearest approximations. Scientific notation has made it easier to write very large or small numbers. You can also use the scientific notation calculator. Therefore, it is used by scientists to write experimental measurements.
For example, Earth has a surface area of 5,101,000,000 miles2, which is a very large number. In scientific notation we can write it as: 5.101 × 109 miles 2 In scientific notation, every non-zero number can be written in the form of
$$m\;×\;10^n$$
The non-zero number is also called a significant figure.
What is the Order of Magnitude?
The order of magnitude gives the idea about a measurement that tells how big or small it is from another measurement. This concept is based on the scientific notation and it is defined as the power of 10 which is closest to the magnitude of that measurement. 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,
$$N\;=\;n\;×\;10^x$$
For example, the surface area of the Earth is written as
$$5,101,000,000\;=\;5.101\;×\;10^9\;miles^2$$
It is the scientific notation of surface area and we say that it has 9 orders of magnitude. The power of 10 refers to the order of magnitude.
What is the difference between scientific notation and order of magnitude?
Scientific notation and the order of magnitude are used to approximate and compare two or more measurements. Here we will discuss the difference between scientific notation and order of magnitude in the following difference table.
| Difference Table |
| Scientific Notation |
Order of Magnitude |
| It is a way of writing very large and small numbers in a simple organised form. |
It uses the scientific notation to give the idea how much an object is magnified. |
|
The mathematical form of scientific notation
$$N\;=\;m\;×\;10^n$$
|
The mathematical form of order of magnitude is
$$N\;=\;n\;×\;10^x$$ |
| The range of m in scientific notation is
$$1\;<\;m\;≤\;10$$
|
The range of order of magnitude is
$$0.5\;<\;n\;≤\;5$$ |
Scientific Notation Rules
There are some rules of writing a number by using scientific notation.
- The base should be always 10.
- The exponent must be a non-zero integer, that means it can be either positive or negative.
- The absolute value of the coefficient is greater than or equal to 1 but it should be less than 10.
- Coefficients can be positive or negative numbers including whole and decimal numbers.
- The mantissa carries the rest of the significant digits of the number.
Let’s discuss an example of scientific notation by following the above rules.
For example,
The population of the Earth is 7,403,000,000. We will write it in scientific notation.
$$7,403,000,000\;=\;7.403\;×\;10^9$$
Order of Magnitude Rules
There are some rules of finding the order of magnitude for any number. The online order of magnitude calculator also follow the same rules.
- The base should be always 10.
- The exponent must be a non-zero integer, that means it can be either positive or negative.
- The absolute value of the coefficient is greater than or equal to 0/5 but it should be less than 5.
- Coefficients can be positive or negative numbers including whole and decimal numbers.
- The mantissa carries the rest of the significant digits of the number.
Consider the following example to understand the order of magnitude.
For example,
The population of the Earth is 7,403,000,000. We will find its order of magnitude by using scientific notation. So,
$$7,403,000,000\;=\;7.403\;×\;10^9$$
The order of magnitude of Earth’s surface area is 9.
FAQ’s
What do you mean by Order of Magnitude?
The order of magnitude of a measurement is an estimation about it that tells how much it is bigger or smaller from the other measurement. It uses scientific notation to find the order of magnitude.
How do you convert from standard form to scientific notation?
To convert from standard form to scientific notation, you need to place the decimal point after first non-zero number. Count the number of digits that you moved. Write the number of digits as the power of 10 such as, $$m\;×\;10^n$$.
Why do we use Scientific Notation?
Scientific notation allows us to express very small and large numbers in a simple and understandable way. It helps to compare two or more experimental measurements in order to find an approximate measurement.
What is meant by scientific notation in physics?
In physics, it is a scientific way of writing very large and small numbers using significant figures. It converts a number as the power of 10 to express it in a manageable way.
What are the 3 Parts in Scientific Notation?
There are three main parts of scientific notation. These are
- Coefficient
- Base
- Exponent
In the formula of scientific notation, N = m × 10n , m is coefficient, 10 is base value and its power is the exponent value.