Concept of Number and its Standard Form
In the field of mathematics, we frequently have larger and smaller numbers (both in decimal) when calculating answers to certain problems. Errors can always occur in these kinds of computations. Occasionally, the required number of our results is excessive, and sometimes our calculation has a lot of zeros after the decimal point. To avoid such problems, the numbers are expressed in standard form.Archimedes is the one who first introduced and made use of the idea of writing numbers in standard form. By adopting base 10, he established a clear and practical approach for writing small or large fonts quickly and easily. We can write numbers in decimal form, regardless of how big or tiny they are.This article will discuss the significance of the standard form of numbers in mathematics and other sciencesalong with its different examples and applications.
Numbers in Standard Form
Standard form, often known as scientific notation, is the method used in mathematics to express bigger orsmaller numbers precisely. Depending on how negative or positive it is, we apply exponents to the power of
10 in this procedure:
For example, one light year is approximately equal to 6000000000000 miles
The ordinary notation = 6000000000000 miles
Through the definition of Standard Form, we have
One Light year = 6.0 × 10^12 miles
How To Convert Ordinary Numbers into Standard Form?
Here are some steps to follow while writing numbers in standard form:- Put the decimal point after the first non-zero digit of the given number.
- Mention “n” digits or the number of digits between the decimal point and the first non-zero digit. In such case, it will be written as 10^n
- The sign "n" is determined by the number that has to be standardized. The number will be expressed as 10^n if the decimal point is moved to the left, and as 10^-n if it is moved to the right, neglecting all zeroes.
What is the procedure for standardizing a whole number?
There are no decimal points as far as whole numbers are concerned. To standardize this, we add a decimal point (.) to the last of the given value. The value of " n" will then be that many digits as we proceed to the left until the first two digits. In whole numbers, n has always positive value.Take the number 52370000000 as an example for standard form.First, we will add a decimal point to a given value, such as 523700000000, after the final digit. Put the decimal point after the first nonzero digit, which is "5", in the second step. The result will be 5.23700000000 × 10^11.
We shall also neglect all the zeros at the end of this figure, giving us the standard form of 5.237 × 10^11.
How a decimal number is standardized?
A decimal point is present in all the decimal numbers, regardless of their format. If there is no decimal point after the one digit or two digits in the provided number, the number will first be standardized by moving the decimal point.For example, write 0.00000129 in standard form.
First, we will put the decimal point after the first non-zero number i.e. ‘3’. Then it will be written as 1.29 ×10^ -6 (as we move the decimal point after 6 digits towards the right)
Example of Standard Form
The distance of Neptune from the sun is approximately 4,472,700,000km. Rewrite this number into standardform.
Solution:
In the first step, we will place a decimal point after the last digit of a given number like 4,472,700,000km.
In the second step, move the decimal point after the first non-zero digit mean ‘6’.
It will become 4.472700000 × 10 9 .
We neglect all the zeros at the last of this number, and then its standard form will become 4.4727 × 10^9 km
A standard form calculator can be used for writing larger and smaller numbers in standard form of numbers.
Applications of Standard form of numbers
To calculate various amounts or numbers in our daily lives, we must be able to articulate them simply. In almost all fields of life, we use the standard form of numbers. The following applications include some of its practical usage.
Computer Science and I.T
The standard form helps us to express extremely big or tiny data quantities, memory capacities, or processor speeds in computer science and information technology. It assists in concisely expressing the size of these amounts. While working on it, many computations take place on the computer, and the standard form makes them simple to organize.
Astronomy and Exploration of Space
Astronomers regularly deal with extremely vast distances and masses. They may represent cosmic distances, such as the separation between galaxies or the size of the universe, using the standard form of numbers. Similarly, scientific notation simplifies the depiction of celestial body mass when it is being discussed.
Microbiology and Genetics
Researchers frequently work with very small amounts, such as the number of cells or the concentration of chemicals, in the domains of genetics and microbiology. They can represent these numbers using the conventional form without using a lot of zeros. For instance, the usual form of numbers might be used to indicate the number of bacteria in a culture.
Data Reporting
Standard form is used in reports and publications to represent statistical data and measurements concisely and uniformly. In data analysis, especially when dealing with very large or very small numbers, performing calculations in scientific notation can simplify operations and reduce the risk of errors due to excessive zeros.
Wrap Up
The concept of the standard form of numbers, whether they are whole or decimal, has been explained in the discussion above. Moreover, by following its calculating stages, we may precisely understand how it is represented. We may each directly address relevant issues in daily life by resolving examples of this nature. We may apply this notation anytime we have trouble when writing larger or smaller computations thanks to the debate around its implementation.
