Following the correct guidelines for significant figures is crucial in reporting accurate data that is reflective of the accuracy of the means used to collect it. It follows that the answer to any calculation can be no more nor any less precise than the least precise piece of data involved in the calculation. In this course, we will follow a set of rules meant to a) provide consistency to our significant figures and rounding and b) provide answers that agree, in accuracy and precision, with our measured data. These rules allow us to skip complex, although more accurate, data analysis, and provide us with a workable, functional, and accurate enough method for our purposes.
In this course we will consider significant figures to be: 1) any non-zero digit, 2) zeros within a number (i.e. 305; 1.0056), and 3) trailing zeroes that are not needed to hold the decimal place (i.e. 5.300). Our rules differ slightly from the textbook in regard to trailing zeroes to the left of the decimal place or numbers with trailing zeros that have no decimal place (i.e. 300. or 300). Silverberg rules that trailing zeros with a decimal point after them (i.e. 5,600.) are made significant, but in our set of rules, those zeroes are considered ambiguous, and must be represented in scientific notation to make their significance clear (i.e. 5,600. should be expressed as 5.600X103). In a discussion of which digits are to be considered significant, it is important to note the class of numbers for which significant figure rules can be disregarded. These numbers are absolute quantities (i.e. NOT measured quantities) or "exact" numbers. Examples of exact numbers are 100 cm in 1 m (these are not considered to have 1 significant figure each) or 567 marbles (not considered to have 3 significant figures). They have no bearing (no matter how many or few significant figures they appear to have) on the number of significant figures in a final answer to a calculation. As our course concerns many measured values (especially in lab or in cases where data has been given to us for problem solving), it is important consider and understand what the number of significant figures in those numbers can tell us about their accuracy. A measured value is considered to be accurate to its second to last significant figure, with the last significant figure understood as an estimated value (that last digit is the least precise figure). The number of significant figures in a measured quantity reflects the accuracy of the device/ system and the certainty with which it was measured. The fewer number of significant figures, the less accurate the measuring device can be assumed to be. In the same way that there are rules providing internal consistency in what figures are significant, there are rules for how many significant figures to record when performing measurements. When performing measurements with a digital device, all figures reported should be recorded. In the case of measurement with an analog device, each significant figure given by the calibration marks on the device should be recorded in addition to a final, estimated, digit. For example, on a meter stick that has markings to the centimeter, a length that rests somewhere between 1.23 and 1.24 should …show more content…
The last significant digit is the rounded digit and its value (rounded up or down) is determined by the following digit. A digit rounds up for numbers 5-9 and down for 0-4. [Note: Silverberg has more complicated rules for rounding when the next-place digit is a 5, but in this course we are using the aforementioned system.] For example 4.589 to three significant figures rounds to 4.59, where 4.581 to three significant figures rounds to 4.58.
Consistent adherence to these rules is crucial in this course because of the amount of information contained in significant figures-- the number of significant figures can reveal the accuracy of a calculation, the reliability of data, and the specificity with which it was measured. It follows, then, that under-reporting in significant figures wastes information and over-reporting is, in fact, "lying" about the specificity of measurement and calculation. Both are poor representations of the data collected, and the methods and certainty with which it was found.
Sources: Source Material provided in CPR essay assignment; Prof. Halpin's General Chemistry I Lecture
In this course we will consider significant figures to be: 1) any non-zero digit, 2) zeros within a number (i.e. 305; 1.0056), and 3) trailing zeroes that are not needed to hold the decimal place (i.e. 5.300). Our rules differ slightly from the textbook in regard to trailing zeroes to the left of the decimal place or numbers with trailing zeros that have no decimal place (i.e. 300. or 300). Silverberg rules that trailing zeros with a decimal point after them (i.e. 5,600.) are made significant, but in our set of rules, those zeroes are considered ambiguous, and must be represented in scientific notation to make their significance clear (i.e. 5,600. should be expressed as 5.600X103). In a discussion of which digits are to be considered significant, it is important to note the class of numbers for which significant figure rules can be disregarded. These numbers are absolute quantities (i.e. NOT measured quantities) or "exact" numbers. Examples of exact numbers are 100 cm in 1 m (these are not considered to have 1 significant figure each) or 567 marbles (not considered to have 3 significant figures). They have no bearing (no matter how many or few significant figures they appear to have) on the number of significant figures in a final answer to a calculation. As our course concerns many measured values (especially in lab or in cases where data has been given to us for problem solving), it is important consider and understand what the number of significant figures in those numbers can tell us about their accuracy. A measured value is considered to be accurate to its second to last significant figure, with the last significant figure understood as an estimated value (that last digit is the least precise figure). The number of significant figures in a measured quantity reflects the accuracy of the device/ system and the certainty with which it was measured. The fewer number of significant figures, the less accurate the measuring device can be assumed to be. In the same way that there are rules providing internal consistency in what figures are significant, there are rules for how many significant figures to record when performing measurements. When performing measurements with a digital device, all figures reported should be recorded. In the case of measurement with an analog device, each significant figure given by the calibration marks on the device should be recorded in addition to a final, estimated, digit. For example, on a meter stick that has markings to the centimeter, a length that rests somewhere between 1.23 and 1.24 should …show more content…
The last significant digit is the rounded digit and its value (rounded up or down) is determined by the following digit. A digit rounds up for numbers 5-9 and down for 0-4. [Note: Silverberg has more complicated rules for rounding when the next-place digit is a 5, but in this course we are using the aforementioned system.] For example 4.589 to three significant figures rounds to 4.59, where 4.581 to three significant figures rounds to 4.58.
Consistent adherence to these rules is crucial in this course because of the amount of information contained in significant figures-- the number of significant figures can reveal the accuracy of a calculation, the reliability of data, and the specificity with which it was measured. It follows, then, that under-reporting in significant figures wastes information and over-reporting is, in fact, "lying" about the specificity of measurement and calculation. Both are poor representations of the data collected, and the methods and certainty with which it was found.
Sources: Source Material provided in CPR essay assignment; Prof. Halpin's General Chemistry I Lecture