SIGNIFICANT FIGURES

Significant figures in the measured value of a physical quantity gives the number of digits in which we have confidence. Significant figures may be defined as the reliable digits plus the first uncertain digit are known as significant digits or significant figures. Larger the number of significant figures obtained in a measurement, greater is the accuracy of the measurement and vice-versa.

RULES FOR COUNTING THE SIGNIFICANT FIGURES:

• All the non-zero digits are significant. e.g 1254 has four significant figures

• All the zeros between two non-zero digits are significant, no matter where the decimal point is, if at all. e.g 1004 has four significant figures

•  If the number is less than 1, the zero(s) on the right of decimal point but to the left of the first non-zero digit are not significant. [In 0.00 2308, the underlined zeroes are not significant].

• The terminal or trailing zero(s) in a number without a decimal point are not significant. [Thus 145 m = 14500 cm = 145000 mm has three significant figures, the trailing zero(s) being not significant

•  The trailing zero(s) in a number with a decimal point are significant. [The numbers 8.500 or 0.007900 have four significant figures each.]

• Rounding off the Uncertain Digits

1. Preceding digit is raised by 1 if the insignificant digit to be dropped (the underlined digit in this case) is more than 5, and is left unchanged if the latter is less than 5.

4.356 = 4.36 (on rounding off up to three significant digits)
4.357 = 4.35 (on rounding off up to three significant digits)

1.  But if the insignificant digit is 5 then if the preceding digit is even, the insignificant digit is simply dropped and, if it is odd, the preceding digit is raised by 1.

5.3245 = 5.324 (on rounding off up to four significant digits)
5.3275 = 5.328 (on rounding off up to four significant digits)