6th Class Mathematics Decimals

  • question_answer 5) Write the following decimals as fractions. Reduce the fractions to lowest form. (a) 0.6 (b) 2.5 (c) 1.0 (d) 3.8 (e) 13.7 (f) 21.2 (g) 6.4 TIPS Firstly, write the given decimal into fraction with denominator 10 and then simplify traction to write in lowest form i.e. numerator and denominator have no common factor other than 1.

    Answer:

    (a) We have, \[0.4=0+\frac{4}{10}\] Lowest form \[0.3=\frac{3}{10}\] [\[0.4=\frac{4}{10}\]HCF of 6 and 10 = 2] \[\therefore \] Fraction of \[\frac{4}{10}>\frac{3}{10}\] and lowest form \[\therefore \] (b) We have, \[0.07=0+0\times \frac{1}{10}+7\times \frac{1}{100}\] [multiplying by 10 in numerator and denominator of 2] \[0.02=0+0\times \frac{1}{10}+2\times \frac{1}{100}\] Lowest form \[0.07=\frac{7}{100}\] [\[0.02=\frac{2}{100}\] HCF of 25 and 10 = 5] \[\therefore \] Fraction of \[\frac{7}{100}>\frac{2}{100}\] and lowest form \[\therefore \] (c) We have, \[3=3+\frac{0}{10}+\frac{0}{100}\] \[0.8=0+\frac{8}{10}+\frac{0}{100}\] Fraction of 1.0 as well as lowest form = 1 (d) We have, \[\therefore \] [multiplying by 10 in numerator and denominator of 3] \[0.5=0+\frac{5}{10}\] Lowest form \[0.05=0+0\times \frac{1}{10}+\frac{5}{100}\] [\[0.5=\frac{5}{10}\]HCF of 38 and 10 = 2] \[0.05=\frac{0}{10}\]Fraction of \[\therefore \] and lowest form \[\frac{5}{10}>\frac{0}{10}\] (e) We have, \[\therefore \] [multiplying by 10 in numerator and denominator of 13] \[1.23=1+\frac{2}{10}+\frac{3}{100}\] Lowest form \[1.2=1+\frac{2}{10}+\frac{0}{100}\] [\[1.23=\frac{3}{100}\] HCF of 137 and 10 = 1] \[1.2=\frac{0}{100}\]Fraction of \[\therefore \]and lowest form \[\frac{3}{100}>\frac{0}{100}\] (f) We have, \[\therefore \] [multiplying by 10 in numerator and denominator of 21] \[0.099=0+\frac{0}{10}+\frac{9}{100}+\frac{9}{1000}\] Lowest form \[0.19=0+\frac{1}{10}+\frac{9}{100}+\frac{0}{1000}\] [\[0.099=\frac{0}{10}\]HCF of 212 and 10 = 2] \[0.19=\frac{1}{10}\]Fraction of \[\therefore \]and lowest form\[\frac{1}{10}>\frac{0}{10}\] (g) We have, \[\therefore \] [multiplying by 10 in numerator and denominator of 6] \[1.5=1+\frac{5}{10}+\frac{0}{100}\] Lowest form \[1.50=1+\frac{5}{10}+\frac{0}{100}\] [\[1\therefore 1\]HCF of 64 and 10 = 2] \[1\therefore 1\] Fraction of \[\frac{1}{100}\]and lowest form \[\frac{1}{100}.\]


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