How to Calculate the Scientific Notation of a Number

Scientific notation is another way of writing a very small or a very large number. It consists of two factors. The first factor is between the number 1 and the number 10. The other factor is written in exponential form as a power of 10 (10-7, or 10 to the 7th power, for instance). 8.3 x 108 is written in scientific notation.Note: when two numbers are multiplied to get what is called a product (the answer), the two numbers are referred to as factors.Note also that in this article a hypen (10-5) indicates an exponent, rather than the more common superscript.

Instructions

Difficulty: Moderately Challenging

How to Calculate the Scientific Notation of a Number

1. First, move the decimal point until you have a number between 1 and 10.For instance, to calculate the scientific notation of 378,000, move the decimal point so the number will be 3.78. Notice that this number is between 1 and 10.The other possibilities: 37.8, 378.000, 3780.00, 37800.0 and 378,000 would not work because they are not between 1 and 10. Thus, 3.78 is the first factor.
2. Ask yourself how many places the decimal point was moved to get the first factor. Notice that when there is no visible decimal point, the decimal point is always behind the last digit on the right. Knowing this, one can see that the decimal point was moved 5 places. If the decimal point is moved to the left, then the exponent is a positive number.This means that the second factor is 105 because the exponent (5 in this case) becomes the number of times the decimal point is moved (5 in this case). Thus, 3.78 x 10-5 is the scientific notation for 378,000.
3. Let’s try writing .000378 in scientific notation. Move the decimal point so we will have a number between 1 and 10. The number will be 3.78. Thus, 3.78 is the first factor.
4. Ask yourself how many places the decimal point was moved to get the first factor. In this case, the decimal point was moved 4 places to the right. This means that the second factor is 10-(-4) because the decimal point was moved to the right. If the decimal point is moved to the right, then the exponent is a negative number. Thus, 3.78 x 10-(-4) is the scientific notation for .000378.

Tips & Warnings

• The exponent is a positive number if the decimal was moved to the left.
• The exponent is a negative number if the decimal point was moved to the right.