The students in carrying out additions, subtractions, multiplications and divisions are confronted with the problems of the number of digits to retain in the answer, specially the last figure in a number when measured on a scale is usually an estimated one. Actually all measuring instruments such as metre sticks, clocks and balances have scales which are sub divided into various units and subunits. Suppose, for example a glass rod ‘A’ whose length is to be measured by two different scales which can be seen in the given figure (1.1) Scale (1) is divided only in centimetres while scale (2) is divided in millimetres also.
In scale (1) the length of the glass rod ‘A’ is about 3.6cm. The length of ‘A’ on scale (2) however is3.62cm. Thus the value3.6 cm contains two significant digits while the value 3.62cm contains three significant digits. This show that one factor which is very important in determining the number of significant digits is the accuracy of the measuring instrument and the second factor which also counts is the size of the object to be measured.
For example, an Iron ball has mass 68.35 g and a smaller one nas mass 7.55 g. The first represents four significant digits while the second has only three significant digits. Zero has its own importance in expressing a number, sometimes it is significant and sometimes it is not significant.
RULES FOR DETERMINING SIGNIFICANT FIGURES
Below are given these rules that will help students to determine the number of significant figures:
(i) Non zero digits are all significant; for example 363 has three significant figures and 0.68 has only two significant figures.
(ii) Zeros between non zero digits are significant, for example, 5004 has four significant figures and likewise 20.4 has three significant figures.
(iii) Zeros locating the decimal point in numbers less than one are not significant:
for example, 0.062 has two significant figures and 0.001 has only one significant figure.
(iv) Final zeros to the right of the decimal point are significant; for example, 2.000 has four significant figures and 506.40 has five significant figures.
(v) Zeros that locate the decimal point in numbers larger than one are not necessarily significant; for example, 40 has one significant and 2360 has three significant figures.
Thus significant figures by definition are the reliable digits in a number that are known with certainty. The last digit of a number is generally considered uncertain by ± 1 in the absence of qualifying information. For example the mass of an object can be expressed as 0.01 12g or as 11.2 mg without changing the uncertainty of the mass or the number of significant figures. The mass is still uncertain by ± 1 in the last digit; this can be expressed as 0.0112 ± .0001 g or as 11.2 ± 0.1 mg.