# Examples of how to convert from scientific notation to decimal numbers

Perhaps the best thing to do before exposing some exercises that can serve as an example of the correct way to convert an expression in Scientific Notation into the original decimal number, of which it has been created, is to revise the very definition of this procedure, in order to be able to understand each of the following examples within its just mathematical context.

## Convert from Scientific Notation to Decimal Numbers

In this way, you will have to start by focusing on the very concept of Scientific Notation, which has been explained by Mathematics as the operation whose purpose is to get the abbreviated form of a particular number.

This procedure is generally used in scientific fields, where it is common to have to handle extremely large numbers, or on the contrary, very small ones. Consequently, Scientific Notation allows to conceive a much more practical expression, which will facilitate the processes of registration, operations, and even reduces the margin of error that could be when manipulating numbers with large numbers of elements.

Therefore, the process of converting a quantity expressed in Scientific Notation to a decimal number is exactly the opposite process, that is, it takes an abbreviated form, and is carried back to the decimal number from which it has arisen. As for this procedure it can be used for some specific mathematical purposes, or even to check if certainly the obtained abbreviated expression is correct.

## Steps to convert from Scientific Notation to Decimal Numbers

Likewise, just as the abbreviation of a number to Scientific Notation has a procedure that must be followed by a scientific method, the reversal must also be carried out following specific steps, which will surely lead to obtaining the correct form, this being understood as the decimal number that totally corresponds to the scientific Notation from which it is based. Next, each one of the necessary steps to carry out this procedure:

1. The first thing that should be done in case of having to deal with an exercise in which scientific Notation should be taken to a decimal number is to revise the sign that accompanies the exponent of the base power 10, since this is the one that will indicate if the number that has been abbreviated previously is a positive or negative number. Ergo, the exponent sign is the one that indicates where the comma should move when starting the conversion. In the case of decimal numbers, the exponent of base 10 will be negative, indicating that the comma should move to the left.
2. Secondly, once it has been corroborated that the original number is certainly a decimal number, the conversion will begin. To do this, take the number by which you multiply the base power 10, and move its comma, to the left, as many times as the exponent value indicates, so you have to fill these places with zeros.
3. Finally, it is verified that certainly the comma has remained to so many places of the first number different from zero that is in the incomplete units of the decimal number, as value has the exponent to which the power of base 10 is elevated.

## Examples of how to convert Scientific Notation to decimals

However, perhaps the best way to study this procedure is through some concrete examples, which allow us to see in practice how it really is that every procedure should be carried out, aimed at converting an expression in Scientific Notation to its original decimal number. Here are some of them:

## Example 1

Convert the following scientific notation to its original decimal number: 3.4 . 10-9

Once the expression is given in scientific notation, we begin by checking the sign of the exponent of base 10, to check that in effect the original number is a decimal number, that is, a number composed by an integer and another decimal, which are separated by a comma, because even if the number that multiplies the power of base 10 is a decimal, if the sign is positive, then the original number will be an integer.

Having done this, and verified that the number being searched for is a decimal, take the figure that multiplies the power of ten, and run its comma nine places to the left, completing each place, in addition to the 3, with zeros. When this number is reached, the comma is written down, and zero is also placed in the whole part of the decimal number found:

3,4 . 10-9 → 0,0000000034

## Example 2

Convert the following scientific notation to a decimal number: 4 . 10-1

This example is ideal to see how even if the number that multiplies the base power 10 is an integer, while the power is elevated to a negative number, the number from which the scientific notation comes will be a decimal number. It also shows how although the base power 10 is raised to -1, the comma should move this number of places to the left. In this way you will have the following conversion:

4 . 10-1 → 0,4

## Example 3

Convert the following scientific notation to a decimal number: 3,25 . 1012

Also in this case, to begin the conversion, it will be necessary to check the sign of the exponent, to corroborate if in effect it is negative, and the number searched for is a decimal. In doing so, it is discovered that this is not the case. Therefore the conversion of scientific notation to an original number can be done, but this number will be integer, even though the number that multiplies the power of 10 is a decimal, since the one that marks the nature of the number from which the scientific notation has come out is the sign of the exponent of the base 10:

3,25 . 1012 → 3250000000000

## Other examples

Among other examples that can be presented on exercises of conversion of scientific notation to decimal numbers, the following will be found:

3,9 . 10-2 → 0,039

9,44 . 10-5 → 0,0000944

1,23 . 10-14 → 0,0000000000000123

5 . 10-9 → 0,000000005

2,5 . 10-20 → 0,000000000000000000025

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Examples of how to convert from scientific notation to decimal numbers
Source: Education
October 31, 2019