Common Core Standards: Math
4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.
Students should be aware that we can write really big or really small numbers as single digits times a power of 10. We call this scientific notation.
The basic idea is that a number containing a lot of zeros at the end can be rewritten as the product of a number between one and ten and a power of 10. It's so much easier, for example, to write 5 × 1011 than to write 500,000,000,000. And when those numbers are used in computation, using scientific notation is an excellent way to save your time and effort.
Students should already know how to convert numbers into this format. They should also understand that they can't multiply any number by a power of 10 and have it be scientific notation. The number has to be between 1 and 10. Be sure they can also convert numbers like 24,900,000 and 0.0000617 into proper scientific notation. (Those are 2.49 × 107 and 6.17 × 10-5 in case you were wondering).
It's also important that students make use of scientific notation and understand appropriate units. For instance, a distance of 3.1 × 107 millimeters would probably best be expressed in kilometers (that makes sense considering that 1 × 106 mm = 1 km).