THE LANGUAGE OF SCIENCE IS NUMBERS AND UNITSBoth the number and the unit are important.A number without a unit is meaningless
LET’S TALK ABOUT THE NUMBER PART FIRST… What is the volume of the following graduated cylinder?
The total number of digits used to express such a measurement is called the number of significant figures. To indicate the precision of a measurement, the value recorded should use all the digits known with certainty, plus one additional estimated digit that usually considered uncertain by plus or minus 1. No further, insignificant, digits should be recorded. All but one of the significant figures are known with certainty. The last significant figure is only the best possible estimate.
SOUNDS EASY BUT HERE’S THEPROBLEM….. What if the measurement is 100g……. Do I mean somewhere between 0 & 200g (1 sig fig)? Do I mean somewhere between 90 & 110g (2 sig figs)? Do I mean somewhere between 99 & 101g (1 sig fig) ? What is the real degree of precision of the measurement?
RULES FOR DETERMINING THE NUMBER OF SIGNIFICANT FIGURES RULE 1 When reading a measured value, all nonzero digits should be counted as significant Example - 136 has 3 sig figs .47 has 2 sig figs RULE 2 Zeros between two nonzero digits are always significant regardless of the location of the decimal place Example - 94.072 g has 5 sig figs
RULE 3 Zeros to the right of the decimal and the left of a nonzero digit are not significant. They are place holders and act to locate the decimal point. Example - 0.0834 cm has 3 sig figs 0.02907 mL has 4 sig figs RULE 4 Zeros at the end of a number and after the decimal point are significant. It is assumed that these zeros would not be shown unless they were significant Example - 138.200 m has 6 sig figs. If the value were known to 4 significant figures, we would write 138.2 m.
RULE 5 Zeros at the end of a number and before an implied decimal point may or may not be significant. We cannot tell whether they are part of the measurement or whether they act only as place holders Example – Back the number 100g, does it have 1, 2, or 3 sig figs?
HOW MANY SIG FIGS ARE IN THE FOLLOWING NUMBERS ? 305 0.0056 305.0 0.00405 305.050 0.003020 250 2.0 250.0 2000003 250.07 0.0000023