Question 1: Convert each of the following fractions into a decimal:

(i) \frac{3}{8}     (ii) \frac{15}{16}     (iii) \frac{101}{25}     (iv) \frac{9}{16}     (v) \frac{13}{40}     (vi) \frac{45}{32}

Answer:

(i) \frac{3}{8} = 0.375           (ii) \frac{15}{16} = 0.9375           (iii) \frac{101}{25} = 4.04

(iv) \frac{9}{16} = 0.5625           (v) \frac{13}{40} = 0.325           (vi) \frac{45}{32} =1.40625

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Question 2: Round off:

(i) 0.00105 , correct to 4 decimal places

(ii) 10.749 , correct to 2 decimal places

(iii) 47.4535 , correct to 3 decimal places

(iv) 182.06451 , correct to 2 decimal places

Answer:

(i) 0.00105 , correct to 4 decimal places = 0.0011

(ii) 10.749 , correct to 2 decimal places = 10.75

(iii) 47.4535 , correct to 3 decimal places = 47.454

(iv) 182.06451 , correct to 2 decimal places = 182.06

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Question 3: Express each of the following as a decimal correct to 3 decimal places :

(i)  \frac{3}{7}           (ii)  \frac{14}{19}          (iii) \frac{19}{21}          (iv) \frac{20}{23}

Answer:

(i)  \frac{3}{7} = 0.429      (ii)  \frac{14}{19} = 0.737      (iii)  \frac{19}{21} = 0.905      (iv)  \frac{20}{23} =0.870

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Question 4: Express each of the following as a recurring decimal. State in each case, whether it is a pure or a mixed recurring decimal:

(i) \frac{1}{6}      (ii) \frac{2}{11}      (iii) \frac{3}{7}      (iv) \frac{8}{18}

Answer:

(i) \frac{1}{6} =1\dot{6} ̇This is a mixed recurring decimal.

(ii) \frac{2}{11} =0.\overline{18} This is a pure recurring decimal.

(iii) \frac{3}{7} =0.\overline{428571}   This is a pure recurring decimal.

(iv) \frac{8}{18} = \dot{4} This is a pure recurring decimal.

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Question 5: Convert each of the following decimals into a fraction :

(i) 0.007           (ii) latex 0.0875           (iii) 9.005           (iv) latex 4.096 

Answer:

(i) 0.007 = \frac{7}{1000}

(ii) 0.0875 = \frac{875}{10000} = \frac{175}{2000} = \frac{7}{40}

(iii) 9.005 = \frac{9005}{1000} = \frac{1801}{200}

(iv) 4.096 = \frac{4096}{1000} = \frac{2048}{500} = \frac{1024}{250} = \frac{512}{125}

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Question 6: Express each of the following decimals as a rational number:

(i) 0. \dot{7}      (ii) 0.\overline{36}      (iii) 4.\overline{26}      (iv) 0. 6\dot{3}      (v) 0.22\overline{73}      (vi) 2.1\overline{36}

Answer:

(i) 0. \dot{7}

Let x=0.7777777 \ldots

\Rightarrow 10x=7.777777 \ldots

\Rightarrow 9x = 7 \ or \ x = \frac{7}{9}

(ii) 0.\overline{36}

Let x=0.363636 \ldots

\Rightarrow 100x=36.363636 \ldots

\Rightarrow 99x=36

\ or \ x= \frac{4}{11}

(iii) 4.\overline{26}

Let x=4.26262626 \ldots

\Rightarrow 100x=426.262626 \ldots

\Rightarrow 99x=422

\ or \ x= \frac{422}{99}

(iv) 0. 6\dot{3}

Let x=0.63333333 \ldots

\Rightarrow 10x=6.3333333 \ldots

\Rightarrow 100x=63.333333 \ldots

\Rightarrow 90x=57

\ or \ x= \frac{19}{30}

(v) 0.22\overline{73}

Let x=0.227373737373 \ldots

\Rightarrow 100x=22.73737373737 \ldots

\Rightarrow 10000x=2273.7373737373 \ldots

\Rightarrow 9900x=2251

\ or \ x= \frac{2251}{9900}

(vi) 2.1\overline{36}

Let x=2.13636363636 \ldots

\Rightarrow 10x=21.3636363636 \ldots

\Rightarrow 1000x=2136.36363636 \ldots

\Rightarrow 990 x = 2115

\ or \ x = \frac{2115}{990} =   \frac{235}{110}

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Question 7: Write the following fractions in descending order by converting them into decimals:

(i) \frac{8}{25} , \frac{4}{15} , \frac{9}{20} , \frac{3}{8} , \frac{11}{16}

(ii) \frac{11}{15} , \frac{12}{17} , \frac{29}{14} , \frac{17}{24} , \frac{14}{19}

Answer:

(i) \frac{8}{25} , \frac{4}{15} , \frac{9}{20} , \frac{3}{8} , \frac{11}{16}

\Rightarrow 0.3200, 0.2667, 0.4500, 0.3750, 0.6875

Now arranging in descending order: \frac{11}{16} , \frac{9}{20} , \frac{3}{8} , \frac{8}{25} , \frac{4}{15}

(ii) \frac{11}{15} , \frac{12}{17} , \frac{29}{14} , \frac{17}{24} , \frac{14}{19}

\Rightarrow 0.7333, 0.7059, 2.0714, 0.7083, 0.7368

Now arranging in descending order: \frac{29}{14} , \frac{14}{19} , \frac{11}{15} , \frac{17}{24}, \frac{12}{19}

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Question 8: Find the H. C.F. and L.C.M. of:

(i) 0.63, 1.05, 2.1      (ii) 1.08, 0.36, 0.9     (iii) 0.3, 0.03, 3     (iv) 1.75, 5.6, 7

Answer:

(i) 0.63, 1.05, 2.1

Convert the numbers into like decimals i.e. 0.63, 1.05, 2.10

First find HCF and LCM of 63, 105 , and 210

HCF = 21

LCM = 630

Therefore HCF and LCM of 0.63, 1.0 5, and 2.1 is 0.21 and 6.30 respectively.

(ii) 1.08, 0.36, 0.9

Convert the numbers into like decimals. i.e. 1.08, 0.36, 0.90

First find HCF and LCM of 108, 36 , and 90

HCF = 18

LCM = 540

Therefore the HCF and LCM of 1.08, 0.36 and 0.9 is 0.18 and 5.40 respectively.

(iii) 0.3, 0.03, 3

Convert the numbers into like decimals 0.30, 0.03, 3.00

Find HCF and LCM of 30, 3 and 300

HCF = 3

LCM = 300

Therefore the HCF and LCM of 0.3, 0.03 and 3 is 0.03 and 3.00 respectively.

(iv) 1.75, 5.6, 7

Convert the numbers into like decimals i.e. 1.75, 5.60, 7.00

Then find the HCF and LCM of 175, 560 and 700

HCF = 35

LCM = 2800

Therefore the HCF and LCM of 1.75, 5.6 and 7 is 0.35 and 28.00