While calculating solutions to some problems, we often have larger numbers as well as smallest numbers (in decimal). Sometimes our outcome is too long and sometimes there are a lot of zeros after the decimal point occurs in our calculation. There is always a chance of error in such kinds of calculations. To overcome these situations, numbers are written in the standard form.
The concept of writing numbers in standard form is first given and used by Archimedes. He introduced a concise and convenient method of writing small or large in the easiest way by using base 10. Through this method, now we can write the numbers in the simplest form whether the number is bigger or smaller (in decimal). In this whole discussion, we will describe the standard form of numbers and the way to convert ordinary notated numbers into standard form in detail.
Table of Contents
What is the Standard Form of a Number?
In Math, the term standard form is defined as the way to represent large or small numbers in a scientific way often called scientific notation. In this process, we use exponents in the power of 10 depending on how negative and positive it is.
For example, the mass of the sun
Ordinary form of number = 1989100000000000000000000000000
Here, using the standard form of the number, we have
Standard form of number = 1.9891 × 1030
How to convert ordinary numbers into standard form?
You can take assistance from an online standard form calculator by MeraCalculator to convert numbers in standard notation. Below are the steps to write number in standard form manually.
- Move the decimal point after the number’s first non-zero digit.
- Say n digit or the number of digits between the first non-zero digit and the decimal point. Then it will be written as 10n.
- The sign with ‘n’ depends upon the number which has to be standardized. If we move the decimal point to the left then it will be written as 10n and it will be written as 10-n, if the decimal point move towards the right also neglects all zeroes.
How to standardize a whole number?
As far as whole numbers are concerned, there is no decimal point in it. For this, we place a decimal point after the last digit of a given number. Then as we move towards the left side till the first two digits, the value of ‘n’ will be that number of digits. The value of ‘n’ always remains positive in whole numbers.
For example, write 5648000000 in standard form.
First, we will place a decimal point after the last digit of a given number like 5648000000. Secondly, move the decimal point after the first nonzero digit meaning ‘5’. It will become 5.648000000 × 109. We also will neglect all the zeros at the last of this number, then its standard form will become 5.648 × 109
How to standardize a decimal number?
As far as decimal numbers are concerned, there exists always a decimal point in it. If in the given number, the decimal point is not present after the first two digits, then first of all we will place the decimal after the first two digits, then it will be standardized.
For example, write 0.0000000349 in standard form.
First, we will place the decimal point after the first non-zero digit i.e. ’3’. Then it will be written as 3.49 × 10-8 (as we move the decimal point after 8 digits towards the right)
Examples
Example 1: Our Earth is one of the planets of the solar system. The mass of Earth is approximately 6000000000000000000000000 kg. Write the mass of Earth in standard form.
Solution:
First, we will place a decimal point after the last digit of a given number like 6000000000000000000000000. Secondly, move the decimal point after the first non-zero digit mean ‘6’. It will become 6.000000000000000000000000 × 1024. We also will neglect all the zeros at the last of this number, then its standard form will become 6.0 × 1024kg.
Example 2: In the structure of an atom, the electron is one of the particles present in it. The mass of a proton is approximately 0.0000000000000000000000000009109384 grams. Write it in standard form.
Solution:
First, we will place the decimal point after the first non-zero digit i.e. ’9’. Then it will be written as 9.109384 × 10-28 grams (as we move the decimal point after 28 digits towards the right)
Applications of Standard form of numbers
In our daily life, we have to express many quantities or numbers easily so that we to understand them easily. The standard form of number is widely used in almost every aspect of life. Some of its daily life applications are given below:
- Computer Science and I.T:
In computer science and information technology, the standard form assists us to represent extremely large or small data sizes, memory capacities, or processing speeds most easily. It helps in conveying the magnitude of these quantities in a condensed format.
Many calculations occur there in the computer while working on it, the standard form makes them easy to sort out.
- Astronomy and Exploration of Space:
Astronomers frequently deal with very large distances and masses in their research. The standard form assists them to express astronomical distances, such as the distance between galaxies or the size of the universe, using feasible numbers.
Similarly, when discussing the mass of celestial bodies, scientific notation simplifies the representation of it.
- Microbiology and Genetics:
In the fields of microbiology and genetics, researchers often experience very small quantities such as the number of cells, or the concentration of substances. The standard form enables them to express these values without writing numerous zeros.
For instance, the number of bacteria in a culture could be represented in terms of the standard form of numbers.
Conclusion
In the above discussion, we have discussed the definition of standard form of numbers whether these are whole or decimal. Moreover, through its calculating steps, we can easily understand its representation accurately.
By solving such kinds of examples, we can personally solve relevant problems in daily life. The discussion about its application will enable us to use this notation anywhere we face difficulty while writing bigger or smaller calculations.