Scientific notation is the process of representing any given number as the product of a number y, where 1<=y<10, and a power of ten. For example, the number 1000 becomes . In this example, the number 1.0 is called the mantissa and the power of ten is the exponent .
When multiplying numbers in scientific notation, the first step is to multiply the mantissas to find the new mantissa and then to add the exponents to find the new power of ten. The new mantissa may be greater than or equal to ten, in which case it is necessary to change the exponent to place the mantissa in the appropriate range.
Example:
The procedure for dividing is similar, except the mantissas are divided and the exponents are subtracted.
The first step in the process of adding numbers in scientific notation is to change the exponents of the numbers so that they are equal. Once the exponents are equal, the mantissas can be added as any other number. It may be necessary to convert the mantissa to fall in the appropriate range after the addition is complete.
