Significant figures are numbers that carry a contribution to a measurement and are useful as a tough methodology to spherical a final calculation. For more complicated systems such as the uncertainty of a dosimetry system, or estimating the bioburden of a product, more accurate methods should be used, resembling those present in NIST
What makes a number “significant” or not significant?
All numbers which will not be leading or trailing zeros are considered significant unless the trailing zero comes after a decimal level (i.e. 3.00 would have three significant figures, while 300 would only have 1 significant determine). In the case of a measurement instrument, if the instrument is only calibrated to a sure decimal place, any digit after that calibration range just isn’t considered significant. For instance, if a weight scale is calibrated to the tenths place (0.0), but provides a reading to the hundredths place (0.00), only an estimate of the tenths place may be accurately reported utilizing traditional rounding methods.
Example: A weight scale calibrated to the tenths place reads a weight of 11.35 lbs. The reading could be rounded to the tenths place and reported as 11.4 lbs.
What rules about significant figures ought to be followed when adding and subtracting numbers?
For addition and subtraction, the final outcome may only have the result reported to the identical decimal place because the least precise measurement.
Instance: The size of a building is 372.71 ft. measured using a tape measure calibrated to the hundredths place. The width of the identical building is 174.2 ft measured using a ruler calibrated to the tenths place. What is the perimeter of the building?
What rules about significant figures needs to be followed when multiplying and dividing numbers?
For multiplication and division, the final end result may only have the same number of significant figures as the least exact measurement.
Example: If the mass of a box is measured to be 6.817 kg, and the amount is measured to be 18.39 cm3 what is the density of the box?
How are constants handled when performing calculations with significant figures?
Recall the system for the circumference of a circle is:
C = 2πr
In this equation, the r represents a measurable quantity, the radius of the circle, and π is a constant. In the case of π, we know infinitely many digits past the decimal place, so the least accurate reading could be from our measurement of the radius. Nevertheless, this just isn’t the case for all constants.
In general, when performing calculations with constants, it is greatest to use one more digit than the least precise measurement. So if we calculate the circumference of a circle with a radius of 4.2 in., we’d use 3.14 as a minimum estimate of π (the radius is significant to the tenths place, so for π, we go out one more digit to the hundredths place).
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