Scientific notation, also called standard index notation, is an operation used to represent long numbers using powers of ten. Scientific notation is used to represent very large or very small numbers in a very easy way.

Very large and very small figures or quantities are difficult to work with, which is why scientific notation arises as a way to abbreviate these numbers. This makes it easier to work with such quantities, whether they are very large or small.

Scientific notation is used as a mathematical resource, a simple way to simplify calculations, since large or small numbers are expressed in a more precise way and are represented in powers of base 10. This can represent whole numbers or decimals in said power of 10. In the decimal system, any number can be represented in scientific notation.

Examples of Scientific Notation

Many times, when you are using the calculator, you can get numbers that are too long. Be it a large number, with many figures on the right; or a small amount, with many leading zeros. For this, scientific notation arises, making these numbers easier to interpret and to work with for future calculations.

Scientific notation is a way to easily handle very large or very small numbers commonly used by scientists, mathematicians, physicists, chemists, etc. To use it, there are a series of rules where you must move the comma, or place of the decimal, until you have a number between 1 and 10. Then you must add a power of ten indicating how many places the comma has been moved.

For example: when you have a very small number, instead of writing 0.0000000078, you will write 78 x 10-9

Another example: when you have a very long number, like 5,540,000,000 it becomes 5.54 x 10 (it reads ten to nine).

That is, 5.54 x 10 would be equal to = 5.54 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

So 5.54 x 10 would be an abbreviation of = 5,540,000,000

What is the importance of scientific notation?

Scientific notation was created to have a great advantage in calculations. Of course, it is easier to read a figure with an exponent than to have to count the zeros in that figure. In addition, it is much easier to use them in this way in equations or large calculations that require precision and accuracy.

Thus, very large or very small numbers abbreviated using scientific notation will take up much less space and will be easier to handle simply by multiplying their exponent.

Scientific notation has greatly streamlined mathematical calculations and operations throughout history; Thanks to this, scientists and mathematicians have saved valuable time and made mathematical discoveries that have promoted technologies, advances in computer science, spatial development, etc. People who work in the field of mathematics use this in their day to day, since they manage to handle their calculations much more easily.

But the other hard sciences also use this method to simplify their work, since in almost all areas we will find quantities or numbers that are difficult to work with. By using scientific notation the risk of error is eliminated and thus more accurate results are obtained.

Let’s look at an example of a hard science and how scientific notation makes the job of calculations easier:

How is scientific notation used in chemistry?

In chemistry, as in other sciences, figures must be interpreted that refer to quantities that can be very small, such as that of the nucleus of a hydrogen atom whose radius is 0’000 000 000 000 001 m; or very small like the speed of light in a vacuum which is approximately 300,000,000 m / s.

These figures must be very specific as they are necessary to achieve exact calculations of quantities to be handled. By having exact amounts and simple procedures, you get an accurate result. This is how with scientific notation it is possible to work more comfortably, since quantities can be represented in a simple way.

Rules of scientific notation

To abbreviate figures with the method of scientific notation there is a class of rules that must be followed:

  • First it is important to know that the figures represented in scientific notation consist of two parts:

A x 10

  • A number that only contains units and decimals. It is a real number greater than 1 and less than 10. This is called the coefficient (a).
  • A power of base ten, which must be an integer. This is called the exponent (n).
  • To express a number in scientific notation, the decimal point (or comma) of said number or long figure must be moved until the new form is a number from 1 to 10 (A); and then express the exponent (n) as the number of places where the decimal point was moved.
  • Whether the power of 10 is positive or negative depends on whether you move the decimal to the right or to the left. Moving the decimal to the right makes the exponent negative; moving it to the left gives you a positive exponent.
  • To use scientific notation on a scientific calculator you must use the [EXP] key, which stands for exponent. That is, you must multiply ten times raised to the number of the exponent that must be entered after that key.
  • For scientific notation, fundamental quantities must be used, or those that correspond to the international system of measurements.
  • To divide numbers represented in scientific notation, the exponents must be subtracted. To multiply, the exponents must be added.

Positive scientific notation

Positive scientific notation is used to abbreviate very large numbers or figures that need to be shortened. Abbreviated in the form of scientific notation, a positive exponent will be obtained.

In this case, the decimal point or comma must be moved to the left until obtaining a number between 1 and 10. In this way, a positive exponent will be obtained.

Negative scientific notation

Negative scientific notation is used to represent very small numbers or figures, that is, with many leading zeros (example: 0.0000000000032). Abbreviating to scientific notation, a negative exponent will be obtained, which will be represented as 10.

In this case, the decimal point or comma must be moved to the right until obtaining a number between 1 and 10 and then represent by means of the exponent how many places said point was moved. In this way a negative exponent will be obtained.

How to convert to scientific notation?

Scientific notation converts large numbers into very small, easy-to-work figures. For example, a large figure like 7,340,000,000 can be converted by taking into account that any whole number can have a decimal point. That is to say:

7,340,000,000 = 7,340,000,000.0

That decimal point must be moved, in this case to the left, until obtaining a number that goes from 1 to 10. In this example, 7,340,000,000.0 will become 7.34

Then the base-10 exponent must be added. This is accomplished by counting how many places the decimal point has moved.

In this case, the decimal point has moved about 9 places to the left. This means that 7.34 must be multiplied 9 times ten to get the large number that started with 7,340,000,000.0. These nine times will be expressed in the exponent. That is to say:

7.34 x 10.  = 7.34 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

7,34 x 10.   = 7,340,000,000

In this way it will have been possible to convert or abbreviate a large number into one that is very easy to read and interpret and to use for future calculations.

Samantha Robson
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Dr. Samantha Robson ( CRN: 0510146-5) is a nutritionist and website content reviewer related to her area of ​​expertise. With a postgraduate degree in Nutrition from The University of Arizona, she is a specialist in Sports Nutrition from Oxford University and is also a member of the International Society of Sports Nutrition.

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