Question

write the following in decimal form and say what kind of decimal expansion
$\frac{1}{11}$
$4 \ \frac{1}{8}$
$\frac{3}{13}$
$\frac{2}{11}$
$\frac{329}{400}$
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Answer 1

Write the following in decimal form and say what kind of decimal expansion each has :

(i) ( frac{36}{100} )

(ii) ( frac{1}{11} )

(iii) ( 4 frac{1}{8} )

(iv) ( frac{3}{13} )

(v) ( frac{2}{11} )

(vi) ( frac{329}{400} )

Solution:

begin{tabular}{l} (i) ( frac{36}{100} ) hline end{tabular} ( frac{36}{100}=0.36, ) terminating decimal expansion (ii) ( mathrm{w}_{mathrm{e}} ) have ( frac{1}{11} ) 1. ( =0.090009 ) [ =0.0 overline{0} ] non.terminating repeating decimal expansion. [ begin{array}{l} 4 frac{1}{8}=frac{33}{8} end{array} ] begin{tabular}{l|c} & 4.125 hline & 33 & 32 hline & 10 & 8 hline & 20 & 16 hline & 40 & 40 hline & ( times ) end{tabular} ( 4 frac{1}{8}=frac{33}{8}=4.125, ) teminating decimal expansion. 7.230769230769 ( =0.2307769, ) non-terminating repeating decimal expansion. ( frac{2}{11} ) 1 begin{tabular}{l|l} & 0.1818 hline 11 & 20 cline { 2 } & 11 hline & 90 cline { 2 } & 88 hline & 20 cline { 2 } & 11 hline & 90 & 88 hline & 2 end{tabular} ( frac{2}{11}=0.181818 ldots ) ( =0 . overline{18}, quad ) non.terminating ( quad ) repeating ( quad ) decimal expansion. begin{tabular}{l|c} & 0.8225 hline 400 & 3290 & 3200 hline & 900 hline & 800 hline & 1000 & 800 hline & 2000 & 2000 hline & ( times ) end{tabular} ( frac{329}{400}=0.8225, ) terminating decimal expansion.

Step-by-step explanation:

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