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Mathematics

By actual division, express each of the following rational numbers as a terminating decimal :

(i) 118\dfrac{11}{8}

(ii) 2316\dfrac{23}{16}

(iii) 76125\dfrac{76}{125}

(iv) 10340\dfrac{103}{40}

(v) 1780\dfrac{17}{80}

(vi) 225\dfrac{2}{25}

(vii) 1125\dfrac{1}{125}

(viii) 3091250\dfrac{309}{1250}

Rational Numbers

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Answer

(i) 118\dfrac{11}{8}

By actual division, we have:

1.3758)11.000‾−8.000‾3000−2400‾600−560‾40−40‾0\begin{array}{r} 1.375 \ 8 \overline{) 11.000} \ \underline{-8\phantom{.000}} \ 30\phantom{00} \ \underline{-24\phantom{00}} \ 60\phantom{0} \ \underline{-56\phantom{0}} \ 40 \ \underline{-40} \ 0 \end{array}

∴ 118\dfrac{11}{8} = 1.375

(ii) 2316\dfrac{23}{16}

By actual division, we have:

1.437516)23.0000‾−16.0000‾70000−64000‾6000−4800‾1200−1120‾80−80‾0\begin{array}{r} 1.4375 \ 16 \overline{) 23.0000} \ \underline{-16\phantom{.0000}} \ 70\phantom{000} \ \underline{-64\phantom{000}} \ 60\phantom{00} \ \underline{-48\phantom{00}} \ 120\phantom{0} \ \underline{-112\phantom{0}} \ 80 \ \underline{-80} \ 0 \end{array}

∴ 2316\dfrac{23}{16} = 1.4375

(iii) 76125\dfrac{76}{125}

By actual division, we have:

0.608125)76.000‾−0.000‾76000−75000‾1000−00‾1000−1000‾0\begin{array}{r} 0.608 \ 125 \overline{) 76.000} \ \underline{-0\phantom{.000}} \ 760\phantom{00} \ \underline{-750\phantom{00}} \ 100\phantom{0} \ \underline{-0\phantom{0}} \ 1000 \ \underline{-1000} \ 0 \end{array}

∴ 76125\dfrac{76}{125} = 0.608

(iv) 10340\dfrac{103}{40}

By actual division, we have:

2.57540)103.000‾−80.000‾23000−20000‾3000−2800‾200−200‾0\begin{array}{r} 2.575 \ 40 \overline{) 103.000} \ \underline{-80\phantom{.000}} \ 230\phantom{00} \ \underline{-200\phantom{00}} \ 300\phantom{0} \ \underline{-280\phantom{0}} \ 200 \ \underline{-200} \ 0 \end{array}

∴ 10340\dfrac{103}{40} = 2.575

(v) 1780\dfrac{17}{80}

By actual division, we have:

0.212580)17.0000‾−0.0000‾170000−160000‾10000−8000‾2000−1600‾400−400‾0\begin{array}{r} 0.2125 \ 80 \overline{) 17.0000} \ \underline{-0\phantom{.0000}} \ 170\phantom{000} \ \underline{-160\phantom{000}} \ 100\phantom{00} \ \underline{-80\phantom{00}} \ 200\phantom{0} \ \underline{-160\phantom{0}} \ 400 \ \underline{-400} \ 0 \end{array}

∴ 1780\dfrac{17}{80} = 0.2125

(vi) 225\dfrac{2}{25}

By actual division, we have:

0.0825)2.00‾−0.00‾200−0.0‾200−200‾0\begin{array}{r} 0.08 \ 25 \overline{) 2.00} \ \underline{-0\phantom{.00}} \ 20\phantom{0} \ \underline{-0\phantom{.0}} \ 200 \ \underline{-200} \ 0 \end{array}

∴ 225\dfrac{2}{25} = 0.08

(vii) 1125\dfrac{1}{125}

By actual division, we have:

0.008125)1.000‾−0.000‾1000−0.00‾1000−00‾1000−1000‾0\begin{array}{r} 0.008 \ 125 \overline{) 1.000} \ \underline{-0\phantom{.000}} \ 10\phantom{00} \ \underline{-0\phantom{.00}} \ 100\phantom{0} \ \underline{-0\phantom{0}} \ 1000 \ \underline{-1000} \ 0 \end{array}

∴ 1125\dfrac{1}{125} = 0.008

(viii) 3091250\dfrac{309}{1250}

By actual division, we have:

0.24721250)309.0000‾−0.0000‾3090000−2500000‾590000−500000‾90000−87500‾2500−2500‾0\begin{array}{r} 0.2472 \ 1250 \overline{) 309.0000} \ \underline{-0\phantom{.0000}} \ 3090\phantom{000} \ \underline{-2500\phantom{000}} \ 5900\phantom{00} \ \underline{-5000\phantom{00}} \ 9000\phantom{0} \ \underline{-8750\phantom{0}} \ 2500 \ \underline{-2500} \ 0 \end{array}

∴ 3091250\dfrac{309}{1250} = 0.2472

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