Round-off?

Question

Round-off 87678 to three significant figures.

Answer 1

Hi Sun;

87,700

This is 87678 rounded to the nearest 100th.  Please note, there is NO decimal point.  If there is...

87,700.

then this means that the figure of 87,700. is exact and there are five significant figures.

Without the decimal point, it is understood that this is only an approximation.  We are certain of the figure in thousands and approximate hundredths, but nothing more specific.

Answer 2

I try to figure out your question, Sun. There is difference between regular rounding of numbers (round to nearest ...) and round-off error.
When researchers can not find exact value of some function, or multi-step calculation, or physical value they write approximate numbers and then show the absolute error ε = |a - b| and relative error
        Δ                 Δ
δ = ----- , or δ = ----- • 100% 
        x                 x

ε = | 87678 - 87700 | = 22

       87700 - 87678
δ = ------------------ × 100% ≈ 0.0251 %
             87678