Significant Figures-Applications | Significant Digits | Exact Numbers

What are Significant Figures?

“The significant figures of numbers are digits convey the meaning that contributes to its measurement resolution”. The number 13.2 comprises three significant digits. Non-zero digits are always significant. 3.14159 has 6 significant digits (all the numbers give you useful information). Thus, 67 has 2 significant digits, and 67.3 has three significant digits.

1000 has 1 significant digit (only the one is interesting; you don’t know anything for sure about the units, tens and hundreds of places; the zeroes may just be placeholders; Similarly for decimals, 0.00069 has 2 significant digits (only the 6 and 9 tell us something; the other zeroes are placeholders, only providing information about the relative size). But this rule has an exception, as in the case of 0.000690 has 3 significant digits (that last zero tells us that the measurement was made accurate to that last digit, which just happened to have a value of zero). one thousand six (1006) has 4 significant digits (the one and six are significant, and we have to count the zeroes because they’re between 2 the significant digits).

Application of Significant Figures

These examples can be incorporated into a list of rules for Significant Figures;

  • All non-zero digits are significant: 4.321g has four significant figures.
  • Zeroes between non-zero digits are significant: 1002 kg has 4 figures.
  • Leading zeros to the left of the first non-zero digits are not significant;
  • Trailing zeroes that are also to the right of a decimal point in a number are significant:0.0260 mL has three significant figures.
  • When a number ends in zeroes that are not to the right of a decimal point, the zeroes are not necessarily significant: 140 kilometers maybe 2 or 3 significant figures.

To resolve this confusion presented by the last rule, we can use the standard exponential representation of the numbers. For example,

3.69 × 104 calories (3 significant figures)

3.069 × 104 calories (4 significant figures)

Exact Number

Some numbers are known with certainty like there are 12 inches in a foot or there are 50 students in a class. Such measurements do have scope for uncertainty. Exact numbers are often found as conversion factors or as counts of objects.

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.