The number of significant figures to the answer of subtraction (64.6312 - 64.5899) is :
3
Do the subtraction first.
\(64.6312 - 64.5899 = 0.0413\).
Apply the rule for addition and subtraction. The result is limited by decimal places, not by significant figures. Both inputs are quoted to four decimal places, so the answer is retained to four decimal places: 0.0413.
Now count the significant figures in that result. Leading zeros are never significant — they only fix the position of the decimal point. So in 0.0413 the digits that count are 4, 1 and 3, giving three significant figures.
This question illustrates an important and often surprising point: subtracting two nearly equal numbers destroys precision. Each input carried six significant figures, yet the difference carries only three. The leading digits cancelled, and with them most of the information; only the last few digits survived, and their uncertainty is now a much larger fraction of the answer.
The effect is known as catastrophic cancellation, and it matters well beyond exam arithmetic — it is why analytical procedures avoid computing small differences between large measurements where possible, for instance by measuring the difference directly rather than by subtraction.
The value 6 is the number of significant figures in each original value, and 4 is the number of decimal places retained — both correct answers to different questions.
Hence the result has 3 significant figures.
Similar Questions
The property measured in derivative thermogravimetric analysis (DTG) is :
Analysis of four different samples of an alloy yielded 12.12, 12.14, 12.10 and 12.22% of metal. The mean deviation of the result is :
For the first order consecutive reaction :
Which of the following statement is incorrect ?
A given reaction is fitted into the following Arrhenius form :
K2 = 6.0 × 1014 (S-1) . exp \(\left[-\frac{104.4\ (\mathrm{kJ\,mol^{-1}})}{RT}\right]\)
Value of the rate constant at very high temperature would be :
The following half cell represents, normal hydrogen electrode (NHE) :
If, we discharge the electrochemical cell rapidly, then :
E° value for various ions are as follows :
E°(MnO4-) = +1.51 V
E°(Ag/Ag+) = +0.7996 V
E°(Au/Au+) = +1.692 V
E°(Zn/Zn2+) = -0.761 V
Based on this data, permaganate can be used to oxidize :
Vapour pressure of 0.5 molal solution of non-volatile solute in organic solvent at 30°C would be :
(Given : vapour pressure of pure organic solvent is 100 torr; the molecular weight of organic solvent is 100 g mol-1).
Molar conductance of 0.01 M acetic acid was found to be 16 × 10-4 S m2 mol-1 at 30°C. Molar conductance of H+ and CH3COO- ions at infinite dilution are 350 × 10-4 S m2 mol-1 and 50 × 10-4 S m2 mol-1, respectively at same temperature. What percentage of acetic acid is dissociated at that concentration ?
The variation of Cp with pressure at constant temperature is given by :
Important Questions from Thermodynamics
Two blocks of ice when pressed together join to form one block because
The ratio C p/C vof the specific heats at constant pressure and volume of a monoatomic ideal gas in two dimensions is
The total number of phonon modes in a solid of volume V is \(\int_{\rm{0}}^{{\rm{ω_ D}}} {{\rm{g}}\left( {\rm{ω }} \right)\,} {\rm{dω }}\) = 3N, where N is the number of primitive cells, ω Dis the Debye frequency and density of photon modes is g( ω ) = AV ω2 (with A > 0 a constant). If the density of the solid doubles in a phase transition, the Debye temperature θ D, will
The dispersion relation of a gas of non-interacting bosons in d dimensions is E(k) = ak s, where a and s are positive constants. Bose-Einstein condensation will occur for all values of
Example of thermoplastic among the following is
