How to Multiply With Scientific Notation

The product of two exponential terms is the sum of its exponents with the same base.

Numbers in scientific notation contain two distinct parts: the coefficient, which must be between 1 and 10, and the exponential term 10^n, where n must be an integer. You often must multiply two numbers in scientific notation in math, chemistry and physics class, a task that is more complex than multiplying two regular numbers. To multiply two numbers in scientific notation, multiply the coefficient and the exponential term independently, then combine the two products.

Instructions

1. Multiply the two exponential terms together by keeping the base as 10 and adding the two exponential values together. For example, the product of the exponential terms of 2.2 x 10^3 and 6.5 x 10^-8 is 10^(3 + (-8)), or 10^(3 - 8), or 10^(-5).

2. Multiply the two coefficients together using long multiplication strategies or a calculator. The coefficient in scientific notation is the number before the exponential term 10^x. In the example, multiply the coefficients 2.2 and 6.5 together to get 14.3.

3. Move the decimal of the product from Step 1 one space to the left and increase the value of the exponent by one if the product is 10 or greater. Coefficients in scientific notation must be greater than or equal to 1 and less than 10, so divide the coefficient by 10 if it is greater than 10 and balance out the expression by increasing the exponent by one. In the example, rewrite 14.3 as 1.43 and increase the exponential term by one to -4.

4. Write the product of the two numbers in scientific notation by multiplying the coefficient and exponential term from Step 3. In the example, the product of 2.2 x 10^3 and 6.5 x 10^-8 is 1.43 x 10^-4.

References

• LaSalle University Department of Astronomy: Scientific Notation