Significant Figures: Basic skills

This post covers the basic skills you need to know in order to correctly specify the number of significant figures in a calculation. A work sheet is attached for homework.

Before we start, we need to clarify the language used.

The least significant digit in a measurement is the smallest value you can reliably read or “resolve” from a meter or a dial, or a digital display.  In many applications this is called the  “resolution” of the measuring instrument. Sometimes this is called the “precision” of the measurement. Note: you can’t always trust the value of that last digit so you need to understand the details of how your measuring device  actually works.

Precision: In some industries, precision means how close together successive measurements will be (think of throwing darts at a dart board where most of the darts stick to the board in a cluster but not necessarily at the bull’s eye). In some industries this is called the “repeatability” of the measurement.

Confusing!  — Right?

Accuracy: Accuracy always means how close the measured value is to the true value.  Bull’s Eye!! You might compare your instrument’s value to the true value by measuring a standard traceable to an NIST (National Institute of Standards and Technology) standard.  For example, you may measure your weight on your bathroom scale as 175 pounds but at the doctor’s office you weigh 178 pounds. Which measurement do you think is more accurate?

A word about logarithms: The number to the left of the decimal place in a logarithm gives the power of 10, the number(s) to the right of the decimal place give the “partial” power of 10 which represent the numeric part of the value. Example: log 10 = 1.0, log 20 = 1.30 where the 1 indicates 10^1 and .30 represents the number 2 (i.e. 10^.30 power = 2). The problem here is that the power of 10 is sometimes called the “characteristic” although it is more correctly called the “ordinate”. The number part (to the right of the decimal) is always called the “mantissa”. So…….. ordinate and mantissa ….. or …. characteristic and mantissa !

I know this is very confusing. You just need to establish ahead of time which usage of the words you and your colleagues will be using.

 

Now for the rules thanks to: http://legacy.jefferson.kctcs.edu/users/kaya.muller/Handouts/Significant%20Figures.pdf

Open the link, read the rules, try the sample problems till you feel confident.
Now here’s your homework:
Note: in some of these problems, you won’t be able to determine the number of sig figs so the answer is “ambiguous”.