Significant Figures
Significant Figures in Measurement and Calculations
A successful chemistry student habitually labels all numbers, because the unit is important. Also of great importance is the number itself. Any number used in a calculation should contain only figures that are considered reliable; otherwise, time and effort are wasted. Figures that are considered reliable are called significant figures . Chemical calculations involve numbers representing actual measurements. In a measurement, significant figures in a number consist of:
Figures (digits) definitely known + One estimated figure (digit)
In class you will hear this expressed as "all of the digits known for certain plus one that is a guess."
Recording Measurements
When one reads an instrument (ruler, thermometer, graduate, buret, barometer, balance), he expresses the reading as one which is reasonably reliable. For example, in the accompanying illustration, note the reading marked A. This reading is definitely beyond the 7 cm mark and also beyond the 0.8 cm mark. We read the 7.8 with certainty. We further estimate that the reading is five-tenths the distance from the 7.8 mark to the 7.9 mark. So, we estimate the length as
0.05 cm more than 7.8 cm. All of these have meaning and are therefore significant. We express the reading as 7.85 cm, accurate to three significant figures. All of these figures, 7.85, can be used in calculations. In reading B we see that 9.2 cm is definitely known.
We can include one estimated digit in our reading, and we estimate the next digit to be zero. Our reading is reported as 9.20 cm. It is accurate to three significant figures.
Rules for Zeros
If a zero represents a measured quantity, it is a significant figure. If it merely locates the decimal point, it is not a significant figure.
Zero Within a Number. In reading the measurement 9.04 cm, the zero represents a measured quantity, just as 9 and 4, and is, therefore, a significant number. A zero between any of the other
A successful chemistry student habitually labels all numbers, because the unit is important. Also of great importance is the number itself. Any number used in a calculation should contain only figures that are considered reliable; otherwise, time and effort are wasted. Figures that are considered reliable are called significant figures . Chemical calculations involve numbers representing actual measurements. In a measurement, significant figures in a number consist of:
Figures (digits) definitely known + One estimated figure (digit)
In class you will hear this expressed as "all of the digits known for certain plus one that is a guess."
Recording Measurements
When one reads an instrument (ruler, thermometer, graduate, buret, barometer, balance), he expresses the reading as one which is reasonably reliable. For example, in the accompanying illustration, note the reading marked A. This reading is definitely beyond the 7 cm mark and also beyond the 0.8 cm mark. We read the 7.8 with certainty. We further estimate that the reading is five-tenths the distance from the 7.8 mark to the 7.9 mark. So, we estimate the length as
0.05 cm more than 7.8 cm. All of these have meaning and are therefore significant. We express the reading as 7.85 cm, accurate to three significant figures. All of these figures, 7.85, can be used in calculations. In reading B we see that 9.2 cm is definitely known.
We can include one estimated digit in our reading, and we estimate the next digit to be zero. Our reading is reported as 9.20 cm. It is accurate to three significant figures.
Rules for Zeros
If a zero represents a measured quantity, it is a significant figure. If it merely locates the decimal point, it is not a significant figure.
Zero Within a Number. In reading the measurement 9.04 cm, the zero represents a measured quantity, just as 9 and 4, and is, therefore, a significant number. A zero between any of the other