How to Change Numbers Into and Out of Scientific Notation

Step-by-Step Guide

1. 1

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

   You'll need to start with a very small or a very large number if you want to successfully convert it into scientific notation.
   
   For example, 10,090,250,000,000 is very large;
   0.00004205 is very small.
2. 2

   Step 2: Cross out the original number's decimal point.

   This is the first step to beginning to convert the number into scientific notation.
   
   If you're working with the number
   0.00004205, just write an "x" over the decimal point. , In this case, the first non-zero number is 4, so place the decimal point after the 4 so that the new number reads
   000004.205.
   
   This works for large numbers, too.
   
   For example, 10,090,250,000,000 would become
   1.0090250000000. , Insignificant digits are any zeros that are not in between other, non-zero digits.
   
   For example, in the number
   1.0090250000000, the zeroes at the end are insignificant, but the zeros between the 1 and then 9, and between the 9 and the 2, are significant.
   
   Rewrite this number as
   1.009025.
   
   In the number
   000004.205, the leading zeros are insignificant.
   
   Rewrite this number as
   4.205. , Just write
   4.205 x 10 for now. , In the case of
   0.00004205 to
   4.205, you moved the decimal point over 5 times.
   
   In the case of 10,090,250,000,000 to
   1.0090250000000, you moved the decimal point 13 times. , For
   1.0090250000000, write x
   1013.
   
   For
   4.25, write x
   105. , If your original number was very large, the exponent should be positive.
   
   If your original number was very small, the exponent should be negative.
   
   For example: the very large number 10,090,250,000,000 becomes
   1.009025 x 10 13 while the very small number
   0.00004205 becomes
   4.205 x 10-5. , This depends on how certain you need to be in your answer.
   
   For example,
   1.009025 x 1013 might be better off as
   1.009 x 1013 or even as
   1.01 x 1013, depending on how accurate you need to be.
3. 3

   Step 3: Add a new decimal point to the number so that there's only one non-zero digit in front of it.

4. 4

   Step 4: Rewrite this number to drop any insignificant digits.

5. 5

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

6. 6

   Step 6: Count how many times you moved the original decimal point.

7. 7

   Step 7: Write that number as the exponent over the number 10.

8. 8

   Step 8: Decide if the exponent should be negative or positive.

9. 9

   Step 9: Round your number as much as necessary.

Detailed Guide

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