Scientific notation is a method of writing large or extremely small numbers in an abbreviated form, using powers. In scientific notation, the number will be represented as the product of a number that is between $1$ and $10$ multiplied by $10$ times some power. That is:

$m\times 10^e$

$m$ It will be a number between $0$ and $1$ If $e$ Is a positive integer, the whole expression will be a number greater than $1$ if $e$ Is a negative integer, the whole expression will be a number less than. $1$

Large numbers

Ways to write very large numbers in scientific notation:

We will move our imaginary decimal point that is at the end of the number to a state where we isolate the number that is between $1$ and $10$ .

We will count how many steps we moved the decimal point to the left, the number of steps we get will be a power of $10$

We will multiply the $10$ by the power we found in our number $m$ and arrive at scientific notation.

Small numbers

Ways to write very small numbers in scientific writing:

Move the decimal point to the right until it is placed after a number smaller than $10$.

We will count how many steps we moved the decimal point to the right, the number of steps we got will be the exponent of $10$, only this time in its negative form.

We will multiply the $10$ by the power we found (in negative) in our number $m$ and we will arrive at the scientific notation.

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Scientific notation of numbers

What does it mean?

In certain scientific subjects such as biology and chemistry, for example, there are very large or very small numbers. For example: The mass of the earth is $6,000,000,000,000,000,000,000,000$ Kg. or the radius of a carbon atom is $0.000,000,000,07$ Meters. So that we can express the same numbers in an easy and convenient way without using a lot of numbers, we can use powers.

Scientific notation is a way to present a very large or very small number in a convenient way. In scientific notation, the number will be shown as the product of a number that is between $1$ and $10$ multiplied by $10$ times some power. That is:

$m\times 10^e$

$m$- It will be a number between $0$ and $1$ If $e$ is a positive integer, the whole expression will be a number greater than $1$ if $e$ is a negative integer, the whole expression will be a number less than $1$

Recall, that when we have a decimal number such as: $5.32$ and we move the decimal point one step to the right, we actually multiply the number by $10$. That is, if we multiply $5.32$ by $10$ we get: $53.2$ Similarly, if we move the decimal point one step to the left, we actually divide the number by . $10$

To write large numbers and small numbers comfortably, we will use a power of $10$. You will understand. Let's take for example a number that is not very large: $183$ If we move our imaginary decimal point one step to the left, we actually divide the number by $10$. Therefore, in order not to damage the value of the number, we will have to multiply it $10$ times immediately. That is :

$183=18.3\times 10$

If we move the point one step further, we will have to multiply by $100$. That is: $183=18.3\times 10=1.83\times 100$ We know that$100$ - it is possible to write as $10^2$ Therefore, we can express $183$ as: $1.83\times 10^2$ In the same way if we take a larger number for example: $5,000,000$ we can say that it is equal to: $5\times 1,000,000$ We know that - is equal to Therefore: So how do we write numbers in scientific notation without getting confused? We will start with the scientific notation of large numbers.$1,000,000$$10^6$

$5,000,000=5\times 1,000,000=5\times 10^6$

Large numbers

Ways to write very large numbers in scientific notation:

We will move our imaginary decimal point at the end of the number to a state where it isolates a number that is between $1$ and $10$.

We will count how many steps we moved the decimal point to the left. The number of steps we have taken will be a power of $10$.

We will multiply the $10$ by the power we found in our number $m$ and get the scientific notation.

Let's see this in an example: Let's take the number: $180,000,000$ We will mark an imaginary decimal point at the end of the number and move it to the left until we isolate a number that is between $1$ and $10$:

We move the decimal point eight times. Therefore, $8$ will be the exponent of $10$. We will obtain: $1.8\times 10^8$

Now we will proceed to the scientific notation of small numbers.

Small numbers

Ways to write very large numbers in scientific notation:

Move the decimal point to the right until it is placed after a number less than $10$.

We will count how many steps we moved the decimal point to the right. The number of steps we have taken will be the exponent of $10$, only this time in its negative form.

We will multiply the $10$ by the power we found (in negative) in our number $-m$ We get the scientific notation.

Take for example the number: $0.00654$

We moved the decimal point to the right until it was set after a number greater than $0$. We counted the number of steps and got $3$. Since we moved the decimal point to the right, the exponent of the power will be the number of steps we obtained in negative form, i.e. $-3$.

Therefore, we will obtain $6.54\times 10^{-3}$

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