\displaystyle \textbf{Question 1: }\text{Find the number of significant figures in each of the}
\displaystyle \text{following measurements:}
\displaystyle \text{(i) }8.4\text{ cm}\qquad\text{(ii) }173.5\text{ m}\qquad \text{(iii) }405\text{ g}
\displaystyle \text{(iv) }4.56\text{ m}\qquad\text{(v) }6.005\text{ kg}\qquad \text{(vi) }0.035\text{ km}
\displaystyle \text{(vii) }0.00123\text{ l}\qquad\text{(viii) }71.040\text{ mg}\qquad \text{(ix) }10.010100\text{ g}
\displaystyle \text{(x) }20.00\text{ km}\qquad\text{(xi) }4.500\text{ ml}\qquad \text{(xii) }101.101\text{ cm}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }8.4\text{ cm has two significant figures}.

\displaystyle \text{(ii) }173.5\text{ m has four significant figures}.

\displaystyle \text{(iii) }405\text{ g has three significant figures}.

\displaystyle \text{(iv) }4.56\text{ m has three significant figures}.

\displaystyle \text{(v) }6.005\text{ kg has four significant figures}.

\displaystyle \text{(vi) }0.035\text{ km has two significant figures}.

\displaystyle \text{(vii) }0.00123\text{ l has three significant figures}.

\displaystyle \text{(viii) }71.040\text{ mg has five significant figures}.

\displaystyle \text{(ix) }10.010100\text{ g has eight significant figures}.

\displaystyle \text{(x) }20.00\text{ km has four significant figures}.

\displaystyle \text{(xi) }4.500\text{ ml has four significant figures}.

\displaystyle \text{(xii) }101.101\text{ cm has six significant figures}.
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Round off each of the following measurements correct to}
\displaystyle \text{four significant figures:}
\displaystyle \text{(i) }67.6519\text{ g}\qquad\text{(ii) }5.30854\text{ kg}\qquad \text{(iii) }22.211\text{ km}
\displaystyle \text{(iv) }70.001\text{ cm}\qquad\text{(v) }0.0013795\text{ m}\qquad \text{(vi) }0.0024060\text{ l}
\displaystyle \text{Answer:}
\displaystyle \text{(i) }67.6519\text{ g}
\displaystyle \text{The measurement }67.6519\text{ g has six significant figures}.
\displaystyle \text{To round it to four significant figures, we round it to two decimal places}.
\displaystyle \therefore 67.6519\text{ g}\approx67.65\text{ g, correct to four significant figures}.

\displaystyle \text{(ii) }5.30854\text{ kg}
\displaystyle \text{The measurement }5.30854\text{ kg has six significant figures}.
\displaystyle \text{To round it to four significant figures, we round it to three decimal places}.
\displaystyle \therefore 5.30854\text{ kg}\approx5.309\text{ kg, correct to four significant figures}.

\displaystyle \text{(iii) }22.211\text{ km}
\displaystyle \text{The measurement }22.211\text{ km has five significant figures}.
\displaystyle \text{To round it to four significant figures, we round it to two decimal places}.
\displaystyle \therefore 22.211\text{ km}\approx22.21\text{ km, correct to four significant figures}.

\displaystyle \text{(iv) }70.001\text{ cm}
\displaystyle \text{The measurement }70.001\text{ cm has five significant figures}.
\displaystyle \text{To round it to four significant figures, we round it to two decimal places}.
\displaystyle \therefore 70.001\text{ cm}\approx70.00\text{ cm, correct to four significant figures}.

\displaystyle \text{(v) }0.0013795\text{ m}
\displaystyle \text{The measurement }0.0013795\text{ m has five significant figures}.
\displaystyle \text{To round it to four significant figures, we retain }1,3,7\text{ and }9.
\displaystyle \text{Since the next digit is }5,\text{ we increase the fourth significant digit by }1.
\displaystyle \text{Rounding }9\text{ up gives }10,\text{ so we carry }1\text{ to the preceding digit}.
\displaystyle \therefore 0.0013795\text{ m}\approx0.001380\text{ m, correct to four significant figures}.

\displaystyle \text{(vi) }0.0024060\text{ l}
\displaystyle \text{The measurement }0.0024060\text{ l has five significant figures}.
\displaystyle \text{To round it to four significant figures, we retain }2,4,0\text{ and }6.
\displaystyle \text{Since the next digit is }0,\text{ the retained digits remain unchanged}.
\displaystyle \therefore 0.0024060\text{ l}\approx0.002406\text{ l, correct to four significant figures}.
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{Round off:}
\displaystyle \text{(i) }17.354\text{ g correct to three significant figures}.
\displaystyle \text{(ii) }18.303\text{ mm correct to four significant figures}.
\displaystyle \text{(iii) }5.0811\text{ kg correct to two significant figures}.
\displaystyle \text{(iv) }22.0005\text{ g correct to three significant figures}.
\displaystyle \text{(v) }0.008507\text{ g correct to one significant figure}.
\displaystyle \text{(vi) }0.00195\text{ mg correct to two significant figures}.
\displaystyle \text{Answer:}
\displaystyle \text{(i) }17.354\text{ g}\approx17.4\text{ g, correct to three significant figures}.

\displaystyle \text{(ii) }18.303\text{ mm}\approx18.30\text{ mm, correct to four significant figures}.

\displaystyle \text{(iii) }5.0811\text{ kg}\approx5.1\text{ kg, correct to two significant figures}.

\displaystyle \text{(iv) }22.0005\text{ g}\approx22.0\text{ g, correct to three significant figures}.

\displaystyle \text{(v) }0.008507\text{ g}\approx0.009\text{ g, correct to one significant figure}.

\displaystyle \text{(vi) }0.00195\text{ mg}\approx0.0020\text{ mg, correct to two significant figures}.
\displaystyle \\

\displaystyle \textbf{Question 4: }\text{Round off:}
\displaystyle \text{(i) Rs. }69.51\text{ to the nearest rupee}.
\displaystyle \text{(ii) }18.0555\text{ kg to the nearest gram}.
\displaystyle \text{(iii) Rs. }4059.995\text{ to the nearest paisa}.
\displaystyle \text{(iv) }0.00949\text{ m to the nearest cm}.
\displaystyle \text{Answer:}
\displaystyle \text{(i) Rs. }69.51\approx\text{Rs. }70\text{, to the nearest rupee}.

\displaystyle \text{(ii) }18.0555\text{ kg}=18055.5\text{ g}.
\displaystyle \therefore 18.0555\text{ kg}\approx18056\text{ g, to the nearest gram}.

\displaystyle \text{(iii) Rs. }4059.995\approx\text{Rs. }4060.00 \text{, to the nearest paisa}.

\displaystyle \text{(iv) }0.00949\text{ m}=0.949\text{ cm}.
\displaystyle \therefore 0.00949\text{ m}\approx1\text{ cm, to the nearest cm}.
\displaystyle \\

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