Significant figures determination

The value with the fewest significant figures determines the number of significant figures in a product. 

SAQ 6.3 To highlight the point made above concerning numbers of significant figures, determine the (negligible) difference in [H30+] between two acid solutions, one having a pH of 6.31 and the other 6.32. 

When multiplying or dividing numbers, the total number of significant figures determines the accuracy of the result. 

Example 4.8 illustrates the rules for rounding off and the significant figure determination. 

For each of the following quantities, underline the zeros that are significant figures, determine the number of significant figures in the quantity, and rewrite the quantity using scientific notation (a) 423.006 mL ... 

We round the intermediate answer (in blue) to one decimal place because the quantity with the fewest decimal places (4.8) has one decimal place. Remember For multiplication and division, the quantity xoith the fewest significant figures determines the number cf significant figures in the answer. For addition and subtraction, the quantity zoith the fewest decimal places determines the number of decimal places in... 

What limits the munber of significant digits in a calculation involving only addition and subtraction How are significant figures determined in calculations involving both addition/subtraction and multiplication/ division ... 

Accurate atomic weight values do not automatically follow from precise measurements of relative atomic masses, however, since the relative abundance of the various isotopes must also be determined. That this can be a limiting factor is readily seen from Table 1.3 the value for praseodymium (which has only 1 stable naturally occurring isotope) has two more significant figures than the value for the neighbouring element cerium which has 4 such isotopes. In the twelve years since the first edition of this book was published the atomic weight values of no fewer than 55 elements have been improved, sometimes spectacularly, e.g. Ni from 58.69( 1) to 58.6934(2). 

The numbers 1.8 and 32 are exact Hence they do not limit the number of significant figures in a temperature conversion that limit is determined only by the precision of the thermometer used to measure temperature. 

The isotopic molar masses are precise to five or more significant figures, so we are tempted to express the result with five significant figures. The mass defect is determined by addition and subtraction, however, and two of the isotopic molar masses are known to just three decimal places, so the mass defect is precise to three decimal places, and the... 

In determining the correct number of significant figures, note that the following values are exact 32°F, 1°C/1.8°F, and 1°C/1 K and have an infinite number of significant figures. 

The calculated simplest formula for Vitamin E is C14H24O. The actual simplest formula for Vitamin E is actually C29H50O2. If the original data had been measured to 4 significant figures, we could have determined the formula correctly. 

Note that the number of significant figures in the result is determined by the precision of the mass of 202Hg, because the mass of12C is established by definition as an exact number. 

In each case, we first determine the molar mass of the compound, and then the mass of the indicated element in one mole of the compound. Finally, we determine the percent by mass of the indicated element to four significant figures. 

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