Explanation

(a) \(\frac{\frac{3}{4}(3\frac{3}{8} + 1\frac{5}{8})}{2\frac{1}{8} - 1\frac{1}{2}}\)

\(\frac{3}{4}(3\frac{3}{8} + 1\frac{5}{8}) = \frac{3}{4}(\frac{27}{8} + \frac{13}{8})\)

= \(\frac{3}{4}(\frac{40}{8})\)

= \(\frac{15}{4}\)

\(2\frac{1}{8} - 1\frac{1}{2} = \frac{17}{8} - \frac{3}{2}\)

= \(\frac{17}{8} - \frac{12}{8}\)

= \(\frac{5}{8}\)

\(\therefore \frac{\frac{3}{4}(3\frac{3}{8} + 1\frac{5}{8})}{2\frac{1}{8} - 1\frac{1}{2}} = \frac{15}{4} \div \frac{5}{8}\)

= \(\frac{15}{4} \times \frac{8}{5}\)

= \(6\)

(b) \(\log_{10} 2 = 0.3010 ; \log_{10} 3 = 0.4771\)

\(\log_{10} 1.125 = \log_{10}(\frac{1125}{1000})\)  (Dividing through with 125)

= \(\log_{10} (\frac{9}{8})\)

= \(\log_{10} 9 - \log_{10} 8\)

\(\log_{10} 9 = \log_{10} 3^{2} = 2\log_{10} 3 = 2 \times 0.4771 = 0.9542\)

\(\log_{10} 8 = \log_{10} 2^{3} = 3\log_{10} 2 = 3 \times 0.3010 = 0.9030\)

\(\therefore \log_{10} (\frac{9}{8}) = 0.9542 - 0.9030 = 0.0512\)

\(\approxeq 0.051\) ( 2 significant figures)

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