How to Solve Numerical Problems with Correct Significant Figures – Part 2

Significant figures (sig fig), aka significant digits, are definite digits within a number written in positional notation that carry both reliability and requirement in conveying a specific quantity.


If the number of figures exceeds what the instrument of measurement can resolve when presenting the outcome of a measurement (viz., mass, length, pressure, or volume), only the figures determined by the resolution are reliable; and therefore, considered significant.

Question:

What should be the reported value of the density of a substance having a mass of 24.0 ± 0.5 g and a volume of 2.0 ± 0.1 cm3?

Solution:



Click to enlarge the image

Rules of sig figs:

# All non-zero numbers are significant.

# Zeros between two non-zero digits are significant.

# Leading zeros are NOT significant.

# Trailing zeros to the right of the decimal are significant.

# Trailing zeros in a whole number with the decimal shown are significant.

# Trailing zeros in a whole number with no decimal shown are NOT significant.

# Exact numbers have an infinite number of sig figs.

# For a number in scientific notation: n x 10x, all digits comprising n are significant by the first 6 rules; 10 & x are NOT significant.

Adding or subtract data: The uncertainty in the calculated value is the sum of the absolute uncertainties and the answer should be quoted to the same number of decimal places as the least precise data.

Multiplying or dividing data: The total % uncertainty is the sum of the individual % uncertainties (the absolute uncertainty can then be calculated from the % uncertainty) and the answer should be quoted to the same number of sig figs as the least precise data.

The calculated absolute uncertainty is generally quoted to not more than one sig fig if it is ≥ 2% of the answer and to not more than two sig figs if it is < 2%.

Intermediate values in calculations should not be rounded off to avoid unnecessary imprecision.

Silly significant figures❓ Let Chemaficionado know at mychemistryhomework@gmail.com❗

References:

(1)    Significant figures. Wikipedia. https://en.wikipedia.org/wiki/Significant_figures.

(2)  Brown, C.; Ford, M. Higher Level Chemistry, 2nd ed.; Pearson Education: Harlow, Essex, 2014.

(3)    Ncert. Chemistry : Textbook for Class XI - Part.I; National Council Of Educational Research And Training: New Delhi.

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