Significant figures are numbers that carry a contribution to a measurement and are helpful as a tough technique to spherical a last calculation. For more complicated systems such because the uncertainty of a dosimetry system, or estimating the bioburden of a product, more accurate strategies should be used, similar to 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). Within the case of a measurement instrument, if the instrument is only calibrated to a certain decimal place, any digit after that calibration range isn’t considered significant. For example, if a weight scale is calibrated to the tenths place (0.zero), but provides a reading to the hundredths place (0.00), only an estimate of the tenths place could also be accurately reported using 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.four lbs.
What guidelines about significant figures ought to be adopted when adding and subtracting numbers?
For addition and subtraction, the ultimate result may only have the outcome reported to the identical decimal place because the least exact measurement.
Example: The size of a building is 372.71 ft. measured using a tape measure calibrated to the hundredths place. The width of the same building is 174.2 ft measured using a ruler calibrated to the tenths place. What’s the perimeter of the building?
What guidelines about significant figures ought to be adopted 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 precise 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 formulation 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 beyond the decimal place, so the least accurate reading would be from our measurement of the radius. Nevertheless, this is just not the case for all constants.
On the whole, when performing calculations with constants, it is finest to make use of one more digit than the least exact measurement. So if we calculate the circumference of a circle with a radius of 4.2 in., we’d use 3.14 at least estimate of π (the radius is significant to the tenths place, so for π, we exit one more digit to the hundredths place).
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