Standard form is also known as scientific notation which is a mathematical representation used to show very large or very small numbers in a standardized format and a concise way. It provides a convenient way to write numbers using powers of 10.
The concept of standard form can be traced back to ancient civilizations such as the Egyptians and Babylonians who derived a numerical system to handle large numbers. However, the formalization of scientific notation began during the Renaissance period in Europe.
In this article, we will explain the concept of standard form, its notation, how to derive it, and its applications in various fields. Moreover, to understand the concept of standard form solving different examples.
Standard Form
Table of Contents
The standard form represents a number as a product of a coefficient and a power of 10. The coefficient is a decimal number greater than or equal to 1 and less than 10 while the power of 10 indicates the scale of the number. The general standard form in mathematical form is expressed as.
Standard form = a × 10b
Where “a” represents the coefficient and “b” represents the exponent or power of 10.
How to Write Numbers in Standard Form?
- Identify the non-zero coefficient from the given number, which should be greater than or equal to 1 and less than 10.
- Identify the decimal position or Count the number of places the decimal point needs to move to make the number between 1 and 10.
- If the decimal point moves from left to right then the power sign takes negative and on the other hand if the decimal point move from right to left then the sign of power takes positive.
- Write the coefficient in standard according to the definition followed by “10b” where “b” is the positive or negative number that shows the place the decimal point moved.
For example:
To write 25,000,000 in standard form.
- The coefficient is 2.5 since we move the decimal point seven places from right to left to make it between 1 and 10.
- In the end, 25,000,000 can be written as 2.5 × 107 in standard form.
To write 0.01234 in standard form.
- The coefficient is 1.2 since we move the decimal point two places from left to right to make it between 1 and 10 and the power sign is negative.
- At the end, 0.01234 can be written as 1.2 × 10-2 in standard form.
You can use a standard form converter offered by MeraCalculator to write numbers in standard notation without any effort.
Applications of Standard Form:
Standard form is widely used in various fields due to its ability to represent a large or small number.
- Science and Astronomy: Standard form is essential for expressing distances between planets or galaxies in standard form. It is also used to represent the masses of atoms and subatomic particles.
- Finance and Economics: In financial reports and economic analysis, the standard form is employed to represent large monetary figures such as national debt, GDP, and company revenues.
- Engineering and Technology: Standard form is useful in engineering and technology fields for expressing measurements such as voltage, current, resistance, and capacitance as well as data storage capacities in a convenient way.
- Physics and Chemistry: Standard form plays an exclusive role in physics and chemistry to represent physical constants such as the speed of light, Avogadro’s number, and Planck’s constant in a readable manner.
Examples section:
In this section, we will solve the different examples to understand the concept of the Standard Form.
Example 1:
Write the given number in standard form if the number is 53427.
Solution:
Step 1:
Write the given number from the question.
= 53427
Step 2:
Check the position of the decimal point to find the exponent.
Exponent = 4
Step 3:
The decimal point moves from right to left and places the decimal point after the 1st non-zero digit to find the Coefficient of the standard form.
Coefficient = 5.3427
Step 4:
Write the standard form representation in a general form.
Standard form = a × 10b
Where “a” represents the coefficient and “b” represents the exponent or power of 10.
Step 5:
Put the above values in the above general form.
Exponent = 4, Coefficient = 5.3427
Standard form = a × 10b
Standard form =5.3427 × 104
Thus, that is the required standard form is 5.3427 × 104.
Example 2:
Converting 0.00000054 into standard form
Solution:
Step 1:
Write the given number from the question.
= 0.00000054
Step 2:
Check the position of the decimal point to find the exponent and sign of the exponent.
Exponent = -7
Step 3:
The decimal point moves from right to left and places the decimal point after the 1st non-zero digit to find the Coefficient of the standard form.
Coefficient = 5.4
Step 4:
Write the standard form representation in a general form.
Standard form = a × 10b
Where “a” represents the coefficient and “b” represents the exponent or power of 10.
Step 5:
Put the above values in the above general form.
Exponent = -7, Coefficient = 5.4
Standard form = a × 10b
Standard form =5.4 × 10-7
Thus, that is the required standard form is 5.4 × 10-7.
Note: The exponent sign is negative because the decimal point moves from the left to the right side.
Conclusion:
In this article, we discussed the short idea of the standard form, how to construct it, and its application in daily life. Moreover, for a better understanding of the concept of standard form in detail solved different examples.