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

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

Change Numbers Into and Out of Scientific Notation Step 1

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.

Change Numbers Into and Out of Scientific Notation Step 2

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.

Change Numbers Into and Out of Scientific Notation Step 3

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

Change Numbers Into and Out of Scientific Notation Step 4

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.
Change Numbers Into and Out of Scientific Notation Step 5

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

Just write 4,205 x 10 for now.

Change Numbers Into and Out of Scientific Notation Step 6

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.

Change Numbers Into and Out of Scientific Notation Step 7

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.

Change Numbers Into and Out of Scientific Notation Step 8

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.
Change Numbers Into and Out of Scientific Notation Step 9

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

Change Numbers Into and Out of Scientific Notation Step 10

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.

Change Numbers Into and Out of Scientific Notation Step 11

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.

Change Numbers Into and Out of Scientific Notation Step 12

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.

Change Numbers Into and Out of Scientific Notation Step 13

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

Change Numbers Into and Out of Scientific Notation Step 14

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.

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