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What are significant figures/digits and what are they used for?
Significant figures are numbers that carry a contribution to a measurement and are helpful as a rough method to spherical a closing calculation. For more advanced systems such as the uncertainty of a dosimetry system, or estimating the bioburden of a product, more accurate methods should be used, such as these present in NIST
What makes a number "significant" or not significant?
All numbers which usually are not 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 figure). In 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), however provides a reading to the hundredths place (0.00), only an estimate of the tenths place may be accurately reported using traditional rounding methods.
Instance: A weight scale calibrated to the tenths place reads a weight of 11.35 lbs. The reading can be rounded to the tenths place and reported as 11.four lbs.
What guidelines about significant figures should be followed when adding and subtracting numbers?
For addition and subtraction, the final consequence may only have the end result reported to the same decimal place as the least precise measurement.
Example: The size of a building is 372.71 ft. measured utilizing 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 guidelines about significant figures needs to be adopted when multiplying and dividing numbers?
For multiplication and division, the final end result may only have the identical 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 quantity is measured to be 18.39 cm3 what's the density of the box?
How are constants dealt with when performing calculations with significant figures?
Recall the components 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.
Basically, when performing calculations with constants, it is greatest 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 might use 3.14 at the 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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