How Do You Multiply Scientific Notation?

# How Do You Multiply Scientific Notation?

Multiply the constants in front, and add the exponents together when multiplying numbers written in scientific notation. Use the generic formula for the process, which takes this form: (n x 10^a) x (m x 10^b) = (nm) x 10^(a+b).

1. Multiply the constants together

Consider the example question (4.2 x 10^3) * (2 x 10^6). Multiply the two constants together, getting a product of 8.4. Write this down as the constant portion of the solution.

2. Add the exponents in the two scientific expressions of powers of ten

Write down the sum of the exponents (3 and 6 in the provided example). Finish writing the solution, taking the form 8.4 x 10^9.

3. Shift the decimal points and adjust the exponent as necessary

Consider the example question (8.2 x 10^5) * (4 x 10^2), which has an initial solution of 32.8 x 10^7. Adjust this answer to suit the standards of scientific notation, which only permit one digit to the left of the decimal point. Adjust the exponent upward by one for each space you have to move the decimal point to the left; in this case, the exponent goes up by 1, which gives you a final answer of 3.28 x 10^8.

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