Paragraph for question Nos. 1 to 3 Two quantities x1= (3.0 plus minus 0.1) S.I. unit x2= (6.0 plus minus 0.2) S.I. unit are given and they are combined so that we find value of combination by x'= x1 +x2 and x''= x1 x2/x1+x2 then 1) The greater of the two combinations is? (Answer : (9.0 plus minus 0.3) S.I. unit) 2) The smaller of the two combinations is? (Answer: (2.0 plus minus 0.3) S.I. unit) 3) Relative error in smaller value of combination is? (Answer: 0.05)

Dear Student

When you add or subtract two numbers with errors, you just add the errors (you add the errors regardless of whether the numbers are being added or subtracted).

The relative error in the result of a multiplication is the sum of the relative errors of the two numbers being multiplied.
The relative error in the result of a division is the relative error in the numerator plus the relative error in the denominator.

Therefore

$$\begin{gathered} x\text{'}=x_1+x_2=(3.0 \pm 0.1) + (6.0 \pm 0.2) =9.0 \pm 0.3 \\ Relative error in two numbers \\ ∆x_1 =\frac{0.1}{3.0}=0.033 \\ ∆x_2 =\frac{0.2}{6.0}=0.033 \\ Total error =0.033+0.033 = 0.066 \\ To write the answer with an absolute error, we need to multiply the 18 by the relative error: \\ Value \times relative error = absolute error \\ 18\times 0.066 = absolute error \\ absolute error =1.188 \\ x\text{'}\text{'}=\frac{x_1{x}_2}{x_1+x2}=\frac{(3.0 \pm 0.1)(6.0 \pm 0.2)}{9.0 \pm 0.3}=\frac{(18.0 \pm 1.188)}{\left(9.0 \pm 0.3\right)} \\ Relative error in numerator and denominator \\ \frac{1.188}{18}=0.066 \\ \frac{0.3}{9.0}=0.033 \\ Total error =0.066+0.033 = 0.099 \\ To write the answer with an absolute error, we need to multiply the 2 by the relative error: \\ Value \times relative error = absolute error \\ 2\times 0.099 = absolute error \\ absolute error =0.198 \\ x\text{'}\text{'}=\frac{x_1{x}_2}{x_1+x2}=\frac{(18.0 \pm 1.188)}{\left(9.0 \pm 0.3\right)}=2\pm 0.1 \\ Also the relative error in samller quanity= 0.99 =0.1 (as shown in above calcualtion) \end{gathered}$$

It seems that answer provided by you are not correct.

If you any other concern please raise it.

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