Standard form of numbers is a concise, precise and convenient method to represent complex ordinary numbers for instance (very small or very large numbers) in a simple form that is termed as scientific notation.

The concept of standard form of numbers plays a key role to make complex calculations a very simple, easy and convenient. Standard form of numbers is extensively used in the field of science, mathematics, statistics, engineering, astronomy, cosmology and in many technical works.

In this blog, we will elaborate the idea of standard from of numbers, its definition, steps to write an ordinary number in scientific notation. We will also explore some of its daily life applications where we will be more able to observe that how scientific notation made our complex calculations convenient and easy.

What is Standard Form of Numbers:

A number is said to be expressed in standard form / scientific notation, when it is written as

M x 10^ⁿ, where 1 ≤ M < 10 and n is an integer. 

Here A is a coefficient and it is a decimal number range from equal or greater than 1 but less than 10. Moreover n (power of ten) specifies the scale or order of magnitude.

Steps to Write Number in Standard Form:

Now we will explain how an ordinary number is written in its standard form. Before going to express an ordinary number in standard form, clarify the standard position of the decimal point which is b/w the 1^st two digits of the number. Observe that to express a number in standard form (scientific notation) following steps are to follow.

1. Identify the Coefficient:

• Locate the non-zero digits appearing first in the given number. These non-zero digits will form the coefficient.
• Place the decimal point after the first non-zero digit of the given number

2. Determine the Power of 10:

We count the number of digits to which the decimal point crosses from its original position to come in standard position and this count represent the exponent of 10.

• We write the exponent of 10 positive as 10^ⁿ if the decimal point shifted n places to the left.
•  We write the exponent of 10 negative as 10^^{– n} if the decimal point shifted n places to the right.

3. Write the Number in Standard Position:

• In this step we write the given number in standard position as a product of the coefficient identified in step 1 and the base 10 with its exponent determined in step 2.

A standard notation calculator is an easy to use tool to write numbers in standard form according to the above-mentioned steps. 

Applications of Standard Form of Numbers:

Standard form of numbers is very important and plays a crucial role in the simplification of complex calculations as well as it is very useful for the extreme level calculations. Now we will describe some important applications of standard form of numbers.

1. Engineering and Scientific Notation:

In our daily life, we observe some complex information and data (very large or very small). It is a difficult task to organize such sort of data in ordinary form like the expenditure’s estimation reports required material for different construction projects of big buildings or roads. So, with the help of scientific notation’s concept, we can easily apprehend the data information.

2. Cosmology and Astronomy:

Standard form of numbers is very useful in the study of cosmology and astronomy to represent the complex sort of measurements like the distances of stars, planets, galaxies and the size of the universe. 

3. Chemistry and Physics:

Standard from of numbers is widely used in the in the deep study of sizes of atoms, diameter of nucleus, atomic masses, molecular sizes, shells and sub shells energy level, absorption and emission of heat energy during fusion and fission reaction. So, in this regard scientific notation makes complicated values simple and easy to understand.

4. Finance and Economics:

Scientific notation or standard from of numbers is extensively used during the economics and financial analysis. It represents very large monetary values i.e. national and international debit, GDP’s data, data figures about imports/exports etc. and makes convenient for the exchange rate transections for the sake of payments.

5. In the field of CS and IT:

The concept of standard from of numbers is applied in the field of IT and CS to represent the storage capability of different storage devices as well as memory storage and data transfer rates etc. Since these IT and CS data values are very large, Standard from of numbers makes them very simple and easy to comprehend.

6. Statistical and Mathematical Analysis:

Standard form of numbers is extremely used in statistical and mathematical analysis. It is applied to analyze the complex computations in distributions (normal and binormal distributions), correlation, probabilities, variabilities, regression, SD, numerical analysis, calculus etc. It permits to do manipulations and comparisons easy.

How to write numbers in standard form?

Example 1: 

Express the number 149 600 000 000 in standard form.

Solution:

Step 1: We identify the coefficient i.e. the non-zero digits (1496) will form the coefficient.

Step 2: Place the decimal point after the first non-zero digit i.e. 1.496

Step 3: In this step we count the number of digits after 1. There are 11 digits to which the decimal point has crossed to come in standard position. This will be the exponent of 10 i.e. 10^¹¹.

Step 4: So, the given number in standard form will be expressed as 1.496 x 10^¹¹.

Example 2:

Express the number 0.000 000 000 000 038 in standard form.

Solution: 

Step 1: We identify the coefficient i.e. the non-zero digits (38) will form the coefficient.

Step 2: Place the decimal point after the first non-zero digit i.e. 3.8

Step 3: We count the number of digits before 3. There are 14 digits to which the decimal point has crossed to come in standard position from left to right. This will be the exponent of 10 i.e. 10^^-14. 

Step 4: So, the given number standard form will be expressed as 3.8 x 10^^-14.

Conclusion:

In this article we have explored the idea of standard form of numbers briefly. We’ve discussed the important steps to write an ordinary number in standard form as well as we’ve explored some useful applications of standard from of numbers.

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