Significant figures and graduated scales
When chemists do experiments, they make measurements. These measurements generally involve the reading of a graduated scale. It is common practice to read a graduated scale as accurately as possible. Thus in making a reading
Using the ruler graduated in mm, the length of the blue square should be recorded as 16.2 mm or 16.3 mm. The last digit is a guess, but it is assumed by others who read the measurement that the last digit is uncertain, and that the actual value is 16.2 ± 0.1 mm.
All of the digits that are certain plus the one that is uncertain are referred to as significant figures.
This number of significant figures in a number obtained from a measurement reflects the accuracy to which the measurement was made and is the same irrespective of how the measurement is reported.
The 0.0162 m quoted above shows that leading zeros are not significant; however trailing zeros are significant because, for example, the length of the blue box could measured to be 16.0 mm.
first use the lines, and
then guess the last digit by reading between the lines.
then guess the last digit by reading between the lines.
Using the ruler graduated in mm, the length of the blue square should be recorded as 16.2 mm or 16.3 mm. The last digit is a guess, but it is assumed by others who read the measurement that the last digit is uncertain, and that the actual value is 16.2 ± 0.1 mm.
All of the digits that are certain plus the one that is uncertain are referred to as significant figures.
The 16.2 mm measurement above has three significant figures.
This number of significant figures in a number obtained from a measurement reflects the accuracy to which the measurement was made and is the same irrespective of how the measurement is reported.
The above measurement could be reported in centimeters or meters or kilometres.
1.62 cm or 0.0162 m have the same number of significant figures despite having different numbers of digits after the decimal point.
Likewise the same measurement expressed in km (1.62 × 10–4 km) has the same number of significant digits.
1.62 cm or 0.0162 m have the same number of significant figures despite having different numbers of digits after the decimal point.
Likewise the same measurement expressed in km (1.62 × 10–4 km) has the same number of significant digits.
The 0.0162 m quoted above shows that leading zeros are not significant; however trailing zeros are significant because, for example, the length of the blue box could measured to be 16.0 mm.