Significant Figures and Calculation Result Rounding - Mixed Operations and Scientific Notation

Greetings,

This post features more complex calculations than the last post.  These will be presented in two parts below.

Mixed Operations

These calculations are of the form, n1(n2 + n3)/n4, where n1, n2, n3, and n4 represent positive decimal numbers.  Order of operations is important here.  The sum, n2 + n3, must be determined first according to PEMDAS.  The resulting sum must be rounded to the correct number of decimal places, according to the last post.  Next, the multiplication and division is carried out, with the result rounded to the lowest number of significant figures in the product/quotient calculation.

Scientific Notation

The main point here is that all of the significant figures are in the numerical part of a scientific notation expression: The 10^Exp. part contains no significant figures and only serves to locate the decimal point.  The same reasoning is used to explain why leading zeros (those on the left) of a decimal number (less than 1) are never significant.  There are generally two situations encountered: 1) Adding (or subtracting) scientific notation values and 2) Multiplying (or dividing) scientific notation values.  When adding (or subtracting) scientific notation values, it is best to move the decimal of one value until the same 10^exp term is obtained.  Then, add the decimal parts and include (the now single) 10^exp term.  When multiplying (or dividing) scientific notation values, gather the decimal parts and 10^exp parts together.  Perform the arithmetic on the decimal part (with rounding to the proper number of significant figures) and combine this with the result of exponent math applied to the 10^exp part.

The following graphic summarizes the concepts described above.

The instructions in the above diagram should be used to practice some actual calculations.

That's all for now.  Have a good one!

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