How to switch from scientific notation of a number to classical notation and vice versa

Scientific notation is commonly used in chemistry and physics to represent very large or conversely, very small numbers. Switching from one (classical notation) to another (scientific notation) of notations is not as difficult as it seems.

Steps

Method 1 of 2: Write numbers in scientific notation

Step 1. Start with a very small number or a very large number

It is better to start with a very small number or a very large number if you want to successfully convert to scientific notation. Consider two examples: 10,090 250,000,000 is very large; 0, 00004205 is very small.

Step 2. Remove the comma from the initial number

This is the first step in writing a number in scientific notation. In our second example, 0, 00004205, we just need to put an "x" in place of the comma.

Step 3. Put a new comma after the first non-zero digit of your number

In our case, the first non-zero number is 4, so put a comma after the 4, which gives: 000004, 205.

This system also works for many. With our first example, 10,090 250,000,000 will become 1.0090250000000

Step 4. Rewrite your number by removing any insignificant digits

Non-significant digits are all zeros whose placement (to the left or behind the last digits placed after the decimal point) does not influence the value of the number.

• For example, with 1.0090250000000, all zeros after the 5 are useless and can be removed. On the other hand, the zeros between 1 and 9, and between 9 and 2 are significant. 1, 0090250000000 can be rewritten as follows: 1, 009025.
• With 000004, 205, all zeros before 4 are insignificant. 000004, 205 can be rewritten as follows: 4, 205.

Step 5. Write "x 10" just after the rewritten number

Just write 4,205 x 10 for now.

Step 6. Count how many places you have shifted the original decimal point

In the case of 0, 00004205, to go to 4, 205, you have moved the decimal 5 places. To go from 10,090 250,000,000 to 1.0090250000000, you moved the decimal 13 places.

Step 7. Write this number of squares in superscript of the 10 that has been written

So for 1.0090250000000, write: x 10¹³. For 4, 205, write: x 10⁵.

Step 8. Put a sign to your exponent (negative or positive)

If your original number is a large number, the exponent will be positive. If your original number is a small number, the exponent will be negative.

• For example: the very large number 10 090 250 000 000 becomes 1, 009025 x 10¹³ and the very small number 0, 00004205 becomes 4, 205 x 10^-5.

Step 9. Round up your number (digit) as needed

It will depend on the instructions given to you. For example, 1.009025 x 10¹³ can be rounded to 1.009 x 10¹³ or even at 1.01 x 10¹³, it all depends on the precision you need.

Method 2 of 2: Write numbers in scientific notation in precise numbers

Step 1. See if you need to move the decimal to the left or to the right

If the exponent of "10" is positive, then you will have to move the decimal to the right, if the exponent is negative, it will be to the left.

Step 2. Count how many places you need to move the decimal point

In the case of the number 5, 2081 x 10¹², you will need to move the decimal 12 places to the right. If the exponent is -7, you will move the decimal 7 places to the left.

Step 3. Move the comma, adding zeros as needed

You may have to add zeros either in front of or behind the number, depending on whether you are moving left or right. For the number 5, 2081, if you move the decimal 12 places to the right, you should get: 5208100000000.

Step 4. In case of small number, remember to put the new comma

Step 5. Enter periods or a space for any number greater than 999

Working from right to left, put a space between each group of three digits. For example, 5208100000000 becomes 5 208 100,000,000.