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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 tough method to round a ultimate calculation. For more complicated systems such because the uncertainty of a dosimetry system, or estimating the bioburden of a product, more accurate strategies ought to be used, resembling these found in NIST
What makes a number "significant" or not significant?
All numbers which are usually not leading or trailing zeros are considered significant unless the trailing zero comes after a decimal level (i.e. 3.00 would have 3 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 shouldn't be 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 needs to be followed when adding and subtracting numbers?
For addition and subtraction, the ultimate result may only have the consequence reported to the same decimal place because the least exact measurement.
Example: The size of a building is 372.seventy one ft. measured using a tape measure calibrated to the hundredths place. The width of the identical building is 174.2 ft measured utilizing a ruler calibrated to the tenths place. What's the perimeter of the building?
What guidelines about significant figures must be followed when multiplying and dividing numbers?
For multiplication and division, the ultimate outcome might only have the same number of significant figures because the least exact 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 handled when performing calculations with significant figures?
Recall the method 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. However, this isn't the case for all constants.
In general, when performing calculations with constants, it is best 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 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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