When to Use Scientific Notation

A number should be expressed in scientific notation (with only one nonzero digit to the left of the decimal) under these conditions:

  1. A number with ambiguous zeroes (tailing zeroes in a number without a decimal)

To remove the ambiguity, it MUST be expressed in sci. not.

e.g. It is not clear whether 35000 has 2, 3, 4 or 5 sig.fig. It is not clear whether the three "tailing zeroes" are significant or not. If you mean 35000 to have 3 sig. fig., then it MUST be expressed as 3.50 x 10 4 .
  1. A number that is very small (as a rule of thumb, less than 0.01).

It is tedious and riskier to copy numbers with a string of avoidable zeroes.

e.g. 0.000 000 83 SHOULD be expressed as 8.3 x 10 - 7
  1. A number that is in exponential form for any reason

e.g. 324.3 x 10 - 8 SHOULD be expressed as 3.243 x 10 - 6

Some students indiscriminately express all their numbers in scientific notation because they are too lazy to figure out when it is necessary. Although it is not "wrong" to do so, you should learn when it is appropriate. For example, it would not be appropriate to tell someone to weigh out "2.5 x 10 grams of salt" when "25 grams of salt" would do equally well.

20.0 x 5.0 = _________________ (42 x 10 3) x 2 = ____________

0.004 ¸ 800 = _______________ 22 x 2.0 = _________________