Significant Figures How to work with lab data, and correctly round calculated values

Data recorded in lab will fall into two main categories Qualitative (descriptive) – These are written descriptions that detail your observations in lab. For example, you might describe the color of a solution. Quantitative – numerical counts or measurements – Scientific measurements are always metric – Reported in graphs or tables – These will consist of a number and its label

In Chemistry, the units matter! You must develop the habit of writing your quantitative data as a number + its unit In our lab, you should have recorded a measurement from the triple beam balance. For example, this could have been written as g. Note the presence of the number, including the 1000ths place, and the correct unit of “grams” or “g”

Significant Figures (sig figs) Indicate precision of a measurement. These are the numbers in a measurement which have meaning, versus the numbers which are only place-holders, or are beyond the precision of a given measurement. Recording data …. – Recording the correct number of Sig. figs. in a measurement include the known digits plus a final estimated digit. See the example below cm

Significant Figures How can you tell the number of significant figures in a measurement? – Count all numbers EXCEPT: Leading zeros  This has 2 sig figs Trailing zeros in a number without a decimal point -- 2,500  This also has two sig figs

, Significant Figures Counting Sig. Fig. Examples , sig figs 3 sig figs 2 sig figs

Significant Figures Calculating with Sig. Figs. – Multiply/Divide - The number with the fewest sig figs determines the number of sig figs in the answer. (13.91g/cm 3 )(23.3cm 3 ) = g 324 g 4 SF3 SF

Significant Figures cont’d. – Add/Subtract - The number with the significant figure that is furthest to the left determines the place of the last sig fig in the answer. – Be careful when rounding if a 5 is involved. If the preceding digit is odd, the value is increased by one when rounded. If the preceding digit is even, then the value will stay as it is when rounded 3.75 mL mL 7.85 mL 224 g g 354 g  7.8 mL  350 g 3.75 mL mL 7.85 mL 224 g g 354 g

Significant Figures cont’d. Exact Numbers do not limit the number of sig. figs. in the answer. Counting numbers: 12 students Exact conversions: 1 m = 100 cm “1” in any conversion: 1 in = 2.54 cm

Significant Figures 1. (15.30 g) ÷ (6.4 mL) Practice Problems = g/mL  18.1 g g 0.84 g g 4 SF2 SF  2.4 g/mL 2 SF