Significant Figures : Errors In Measurements

Significant Figures

What are Significant Figures?

“The significant figures of numbers are digits convey the meaning that contributes to its measurement resolution”. The number 13.2 is comprised of 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 place holders; 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 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 nonzero digits are significant: 4.321g has four significant figures.
  • Zeroes between nonzero digits are significant: 1002kg has 4 figures.
  • Leading zeros to the left of the first nonzero 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 kilometres may be 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.

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Practise This Question

Match the order of magnitude of observations in p and q with their correct values in x and y.

(p)3×108                     (x) 8                  

(q)7×108                     (y) 9