Scientific notation is a way of expressing very large numbers into smaller readable numbers. Also called a standard or scientific form, for instance, if we have to deal with a very large number something like 0.0000008. It can be easily written or expressed in a scientific notation as, 8×10-7 here 7 is an exponent.
In this article, we will discuss in detail the history of origin of this notation, its forms and also have a glance at the method to calculate it. Scientific notation is said to be one of the most crucial and important topics in mathematics due to its calculations and concepts. Read on to learn the historical facts of scientific notation and how can we express scientific notation in an more generalized and appropriate way.
Now, let’s get started:
Many years back, for the sake of convenience a standard form was introduced that can make large numbers either decimals or other look and sound easier.
Scientific notation was discovered by a brilliant Greek mathematician known as Archimedes, who was a pioneer in the scientific world. He used his expertise in mathematics to develop a method to calculate the number of grains of sand in the universe for King Gelon.
He computed it as 1 followed by 63 zeros, although the understanding of the universe was different back then. Since, the modern numeral system wasn’t invented yet, so he used Greek letter numerals for the computation of grains.
Even though it is impossible to find the number of sand grains in the universe, this historical event proves that for quite long scientists had a keen interest in quantities with varying size. This enthusiasm of measuring objects like the diameter of a planet to the diameter of an atom, led to the discovery of Scientific notation to make the task much easier.
How to express a number in Scientific Notation?
This notation is a compact form of a very large or small number. It is useful in expressing measurements like distance of earth to moon, or very small objects like diameter of a particle. It is expressed in the form of a power of 10.
For example, the speed of light 300,000,000 meter per second is expressed as 3×108 m/s.
General or Normalized Form of Scientific Notation:
The general form of expressing a number in this notation is a×10b, where b represents an integer termed as the exponent, and a signifies any real number or mantissa.
In this normalized type the real number a must follow 1 ≤ a < 10. In this way, a can be any chosen value from 1 to less than 10, which means it can be 9.99 but not 10.
Moreover, the order of magnitude depends on the exponent. If the value of b is greater, the overall number is larger, the same holds for the smaller exponent in that case the overall number will be smaller.
The Engineering form of notation:
In this form, the exponent b has a restriction, it can only be multiples of 3. Therefore it is not always normalized, the numbers expressed in this form can be read using the magnitude prefixes, much like nano, micro etc.
For instance, a number 10.5 × 10-9 can be easily read as 10 point 5 nanometers or 10.5 nm.
Form using letter E:
Another variation is replacing the number 10 with the letter E. It is used in devices like calculators and some computers, where it is difficult or not programmed to display something like 108. For example, 1.6×1031 can be represented using E as 1.6 E+31.
How to convert a number?
Follow these simple steps to convert a number to scientific notation:
Example: Convert 154.58 into scientific notation
Step 1: Write the number in a form that shows it multiplied by 100
154.58 = 154.58 × 100 (same as multiplied by 1)
Step 2: Now, now divide the real number or mantissa by 100, and shift the decimal two places to the left side.
154.58/102 × 100 × 102 = 1.5458×102
In order to convert 0.00134 multiply the number by 1000 by adding -3 to the exponent. It will look like this, 1.34 × 10-3.
Now, if you are interested in calculating scientific notation with precision, without doing any math work try using an online calculator like scientific notation calculator. Online calculators adds value to the topic and such easily available online tools makes calculations easy. Online calculators are usually fast, reliable and easy to use. But one should not rely on such calculating software as learning the concepts should be the priority. If you want to learn concepts, then you should use online tools for help only so that you could calculate results on run time while studying and learning.
In the end, I hope this article will help you understand the origin and working of this marvelous notation and also assist you in representing huge numbers in this notation. Good luck!