Significant figures | Maths | Education in Chemistry
To determine the number of significant figures in a number use the following 3 rules: .. Finally, if r is close to zero, there is little if any relationship between the variables The term pH means to take the –log10 [H+ concentration] or [H3O+ . Nonzero digits always count as significant figures. 2. Zeros are what mix pH = has only two significant figures and corresponds to a [H+] = x M. When considering significant figures in relation to logarithms, you must appreciate that the A chemistry example would be the calculation of pH, defined by.
However, we know how difficult it is to make trace measurements to 3 significant figures and may be more than a little suspicious. If the value is reported as 0.
A statement of how the uncertainty was determined would add much more value to the data in allowing the user to make judgments as to the validity of the data reported with respect to the number of significant figures reported. This number contains 5 significant figures. However, the atomic weight of boron is It is, therefore, difficult to believe the data reported in consideration of this fact alone.
The zeros to the left of the number are never significant. Scientific notation makes life easier for the reader and reporting the number as 1.
How many sig figs when calculating pH from concentration - CHEMISTRY COMMUNITY
A number reported as 10, is considered to have five significant figures. Reporting it as 1. Reporting an uncertainty of 0.
Mathematical calculations require a good understanding of significant figures. In multiplication and division, the number with the least number of significant figures determines the number of significant figures in the result.
pH and significant figures
With addition and subtraction, it is the least number of figures to the left or right of the decimal point that determines the number of significant figures. Examples The number 1. The product, which is equal to 1. The dividend, which is equal to 1. The addition of 5. Leading zeros, as in 0. Pure integers, such as those arising from stoichiometric ratios, are exact numbers and can be considered to have an infinite number of significant figures. Thus the number two which appears in the chemical equation: Addition and subtraction When two physical quantities are added or subtracted, the answer should be given to the least number of decimal places in the original data.
Thus, if we want to combine the electrode potentials described by the equations: Products and quotients In this case we quote the final answer to the least number of significant figures given in the original data.
Logarithms When considering significant figures in relation to logarithms, you must appreciate that the digits before the decimal point indicate the magnitude of the number, and those after the decimal point its actual value.
Thus, if we are taking the logarithm of a number, the number of significant figures after the decimal point in the resulting value should be equal to that in the original data.Sig Fig rules (Significant Figures)
For example, the log10 of Conversely, if we are taking an antilogarithm, then the number of significant figures in the answer is equal to the number of digits after the decimal point. Somewhat confusingly, leading zeros are treated as significant when we consider the logarithmic values in this case.
Significant Figures and Uncertainty
A chemistry example would be the calculation of pH, defined by: More complicated examples In chemistry we are frequently dealing with equations which require us to combine these rules. At a temperature of For more complicated examples with more steps it may be worth calculating the final value and then revisiting individual steps to consider the appropriate number of figures to carry through at each stage. Often one quantity will be significantly less precise than the others which will make this a much easier process.
Further Reading A method I have found works particularly well to introduce this topic is that described by Clase.
Students are able to appreciate that adding an unknown digit to a known digit results in another unknown digit. Unfortunately, it is less straightforward to illustrate the other rules described above.