Math Skills Review
Scientific Notation and Exponent Manipulation
When a number is very large or very small, it may be difficult to work with in long chemical
calculations. It is easier to write this number in scientific notation. Additionally, when working
with significant figures, scientific notation often helps for rounding correctly.
A number written in scientific notation is comprised of 3 significant features. All numbers in
scientific notation have a single non-zero digit before a decimal point. They are all multiplied by
the 10 and the 10 has an exponent on it.
For a specific example, let’s look at the number 0.00000560.
Written in scientific notation, this number is 5.6 x 106. This is determined by counting the
number of places the decimal has to slide in order to have a non-zero number before the decimal
point. All numbers following the decimal point are significant, even zeroes.
CALCULATIONS INVOLVING NUMBERS IN SCIENTIFIC NOTATION
Addition and Subtraction:
First convert to the same power of 10, then add or subtract the digit terms.
Example: (8.97 x 104) – (2.62 x 103) = (8.97 x 104) – (0.262 x 104) = 8.71 x 104
Note that we keep sig figs to the tenths place!
Multiplication:
First multiply digit terms normally, then add exponents separately.
The end result must be adjusted to be in correct scientific notation.
Example: (3.4 x 106)*(4.2 x 103) = (3.4*4.2) x 10(6+3) = 14.28 x 109 = 1.4 x 1010
Note that we keep only two sig figs, but do the rounding at the end.
Division:
First divide digit terms normally, then subtract the exponents separately.
The end result must be adjusted to be in correct scientific notation.
Example: (6.4 x 106)/(8.9 x 102) = (6.4/8.9) x 10(6-2) = 0.719 x 104 = 7.2 x 103
Note that we keep only two sig figs, but do the rounding at the end.
Powers of Exponentials:
First raise the digit term to the indicated power, then multiply the exponent by the
number that indicates the power.
Example: (2.4 x 104)3 = (2.4)3 x 10(4*3) = 13.824 x 1012 = 1.4 x 1013
Note that we keep only two sig figs, but do the rounding at the end.