Scientific notation is commonly used in chemistry and physics to represent very large or very small numbers. Converting numbers to and from scientific notation isn't as difficult as it sounds. Just follow these steps to find out how to proceed.
Steps
Method 1 of 2: Part 1: Converting Numbers to Scientific Notation
Step 1. Start with a very small or very large number to learn how to properly convert to scientific notation
For example, 10,090,250,000,000 is very large, while 0.00004205 is very small.
Step 2. Mark the decimal point of the original number with a cross
This is the first step to start converting the number to scientific notation. If you are working with the number 0, 00004205, just write an "x" above the comma.
Step 3. Add a new comma to the number, so that there is a single non-zero digit before the comma
In this case, the first non-zero number is 4, so you have to move the comma after the 4: the new number becomes 000004, 205.
This also works for large numbers. For example, 10,090,250,000,000 will become 1, 0090250000000
Step 4. Rewrite this number to eliminate any non-significant zeros, that is, zeros that are on the far right or left of the number
- For example, the number 1, 0090250000000 has zeros at the end which are not significant, while those between 1 and 9 and between 9 and 2 are significant and therefore should not be removed. Rewrite this number as 1, 009025.
- In number 000004, 205, leading zeros are insignificant. Rewrite this number as 4, 205.
Step 5. Write "x 10" after the newly rewritten number
Just write 4, 205 x 10 for now.
Step 6. Count how many spaces the comma has been moved from its original position
In the case of 0, 00004205, the comma has been moved five places to form the number 4, 205. Instead, from 10.090.250.000.000 to number 1, 0090250000000, it has moved 13 places.
Step 7. Write this number as an exponent of the power of 10
For 1, 0090250000000 write x 1013. The other number, on the other hand, is expressed as 4, 25 x 105.
Step 8. Decide if the exponent should be positive or negative
If the original number was very large, the exponent should be positive. If the original number was very small, the exponent should be negative.
For example: the number 10, 090, 250, 000, 000, huge, becomes 1.009025 x 1013, while the infinitesimal number 0, 00004205 becomes 4, 205 x 10- 5.
Step 9. Round off your number just enough
This depends on how precise you need to be in your answer. For example, 1, 009025 x 1013 it could be best expressed as 1,009 x 1013 or even as 1, 01 x 1013, according to the required accuracy.
Method 2 of 2: Part 2: Converting Numbers from Scientific Notation
Step 1. Decide whether you will move the decimal point left or right
If the exponent of 10 is positive, then you will move the decimals to the right; if the exponent is negative, you will go to the left.
Step 2. Write how many places you should move the decimals
In the case of the number 5, 2081 x 1012, you will move twelve spaces to the right. If the exponent is a - 7, you will move left seven places; if the exponent is a 5, you will go right five places.
Step 3. Move the comma, adding a zero for each blank
You may need to add them before or after the number if you move left or right respectively. If you move forward 12 spaces to the right starting from number 5, 2081, the new number becomes 5208100000000.
Step 4. Write the decimal point after moving the correct amount of spaces
Step 5. Put the dots in the thousands to any number greater than 999, in front of each group of three digits starting from the right
For example, 5208100000000 becomes 5,208,100,000,000.
