1. What is the number of significant figures in each of thefollowing measures qu

Question

1. What is the number of significant figures in each of thefollowing measures quantities? (a) 2513 kg (b) 0.0034 g (c) 5.060 mL (d) 0.01060 cm (e) 1.245 x 10-6 L 2. Carry Out the following operations, and express the answerwith the appropriate number of significant figure and units. (a) (5.231 mm)(7.1 mm) (b) 72.3 g/1.2 mL (c) 12.21 g + 0.0132 g (d) 31.03 g + 12 mg 1. What is the number of significant figures in each of thefollowing measures quantities? (a) 2513 kg (b) 0.0034 g (c) 5.060 mL (d) 0.01060 cm (e) 1.245 x 10-6 L 2. Carry Out the following operations, and express the answerwith the appropriate number of significant figure and units. (a) (5.231 mm)(7.1 mm) (b) 72.3 g/1.2 mL (c) 12.21 g + 0.0132 g (d) 31.03 g + 12 mg

Explanation / Answer

In any number, EVERY NON-ZERO DIGIT counts as“significant”. In addition, a “zero”digit is “significant” if there is a non-zero digitBOTH to its right (lower order) and to its left (higher order).

“Leading zero” digits (which separate the firstnon-zero digit from the decimal point) are NOTsignificant. “Trailing zero” digits are also NOTsignificant EXCEPT when the number has an explicit decimalpoint.   In both cases, the “zero” digitmerely serves to locate the decimal point and so the order ofmagnitude of the other non-zero digits. The exception reflects thea trivial but universally accepted practice that when a decimalpoint need not be written (e.g., at the end of a number which is>1), then actually taking the trouble to write it implies thateverything preceding it is significant (measured).

Exponents are not significant. (they merely specify where thedecimal point is).

Seems needlessly complicated, but them’s therules. The convention reflects the presumption that chemistryis an experimental science, and it imbues every number with animplicit experimental precision, which is inherited by everythingarithmetically derived from it.

That is, when numbers are combined in a computation, the resultcannot be any more “precise” than the least precisenumber it was derived from. If you consider the precision ofthe number to be ±1 in the rightmost digit, then the resultof any computation must have the same relative precision. Thisleads to two “rules”:

1. when multiplying/dividing, the product/quotient will inheritsame number of significant as the operand with the smallest numberof significant digits.   (This results in aproduct/quotient with the same % precision).

2. when adding/subtracting, you identify the number for whichthe lowest/”rightmost” significant digit; thelowest/”rightmost” of the result will be in the samecolumn (order of magnitude). This gives a result with“imprecision” of the same order of magnitude.

So your questions are:

(a) 2513 kg    = 4 sig fig

(b) 0.0034 g   = 2 sig fig

(c) 5.060 mL = 4 sig fig

(d) 0.01060 cm    = 4 sig fig

(e) 1.245 x 10-6 L   = 4 sig fig

2. Carry Out the following operations, and express the answerwith the appropriate number of significant figure and units.

(a) (5.231 mm)(7.1 mm)   = 37    (2 sigfig)

(b) 72.3 g/1.2 mL = 60.     (2 sig fig– note the explicit decimal point)

(c) 12.21 g + 0.0132 g = 12.22 (4 sig fig,, but only down to the1/100 column)

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