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# Why are significant figures important when reporting measurements

• for a quantity that is the result of a direct measurement, the number of decimal digits (the number of digits in the representation of the number, both to the right and the left of the decimal point) in that quantity is generally fixed by the measuring device. The number of significant digits can depend on the value of the measurement.
• Our rule of thumb is that, for a device whose output is linear. the eye can estimate values lying between two marks on a scale to one-fifth of the distance between the two marks.
For experimentally determined quantities, the number of significant figures is not simply related to the intrinsic precision of a device. Consider the buret and the analytical balance.

The buret permits a volume to be read to ± 0.02 mL (one-fifth of the smallest division on its scale). How many significant figures does such a quantity have?

• If the volume is less than 1.00 mL, the number of significant figures in the volume is two (e.g. 0.57 mL). If the recorded volume is between 1.00 and 9.99 mL, the number of significant digits is three. If the volume is between 10.00 and 50.00 (the maximum capacity of the buret), the number of significant figures in the volume reading is four -

the maximum number of significant digits which a 50 mL buret is capable of producing.

Buret readings must always be reported to two decimal places. regardless of the volume reading. The number of significant figures in the reading clearly depends on the magnitude of the reading.

Next, consider the analytical balance.

The number of significant figures represented by weights varies with the total weight of an object. Nevertheless, weights determined on an analytical balance must always be reported to four decimal places. regardless of the weight. Again, the number of signficant figures in the weight depends on the weight. E.g.

For weights:

• less than 1 mg (0.0010 g), the balance produces only 1 significant figure (e.g. 0.0006 g = 0.6 mg)
• between 1.0 and 9.9 mg (0.0099 g), the balance produces 2 significant figures (e.g. 0.0066 g = 6.6 mg)
• between 10.0 and 99.9 mg (0.0999 g), the balance produces 3 significant figures (e.g. 0.0666 g = 66.6 mg)
• between 100.0 and 999.9 mg (0.9999 g), the balance produces 4 significant figures (e.g. 0.6666 g = 666.6 mg)
• between 1.0000 g and 9.9999 g, the balance produces 5 significant figures, (e.g. 6.6666 g)
• between 10.0000 g and 99.9999 g, the balance produces 6 significant figures (e.g. 66.6666 g)

Source: www.ic.sunysb.edu
Category: Bank