Scientific notation makes it simpler to multiply and divide large and small numbers. In this section, we focus on multiplication.

When multiplying numbers expressed using scientific notation, you first find the leading value of the result by multiplying the leading values of the numbers in the traditional way. If you want to multiply 2×10³ by 3×10⁴, the leading values are two and three, and their product is six. This is the leading value of the product.

Next, add the exponents to find the power of ten. In the example above, the exponents are three and four. You can add them to get the result 10⁷. The final result of the multiplication is 6×10⁷. The principles of how to multiply numbers in scientific notation and an example problem are shown to the right.

With scientific notation, you should format your number after the multiplication so that the leading value remains between one and 10. In other words, if you multiply 3.0 by 4.0, you should report the value as 1.2×10¹, not 12×10⁰.