# Rules for Multiplying Scientific Notation

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Numbers with multiple zeros can be difficult to record and manipulate. Consequently, scientists and mathematicians use a shorter method to write significantly large or small numbers called scientific notation. Instead of saying the speed of light is 300,000,000 meters per second, scientists can record it as 3.0 x 10^8. Simplifying the numbers makes them not only easier to express, but also easier to multiply.

## Using Scientific Notation

To write a number in scientific notation, you must write it as the product of a number and a power of 10. The first number is called the coefficient, and it must be greater than or equal to 1 and less than 10. The second number is called the base, and it is always written in exponent form. To convert a number to scientific notation, put a decimal after the first digit. This becomes the coefficient. Then, count the number of places from the decimal to the end of the number. This number becomes the exponent. For the number 987,000,000,000, the coefficient is 9.87. There are 11 places after the decimal, so the exponent is 11. In scientific notation, it is 9.87 x 10^11.

## Simple Multiplication

To multiply numbers in scientific notation, first multiply the coefficients. Then, add the exponents of the two numbers and keep the base 10 the same. For example (2 x 10^6) (4 x 10^8) = 8 x 10^14.