question_answer 1)

Write each of the following as decimals. (a) \[=30+\frac{2}{100}+\frac{5}{1000}=30+0.02+0.005=30.025\] (b) \[2\times 100+1\times 10+1\times 1+9\times \frac{1}{10}+0\times \frac{1}{100}+2\times \frac{1}{1000}\] (c) \[=200+10+1+\frac{9}{10}+0+\frac{2}{1000}=211+\frac{9}{10}+\frac{2}{1000}\] (d) \[=211+0.9+0.002=211.902\] (e) \[0\times 100+1\times 10+2\times 1+2\times \frac{1}{10}+4\times \frac{1}{100}+1\times \frac{1}{1000}\] (f) \[=0+10+2+\frac{2}{10}+\frac{4}{100}+\frac{1}{1000}=12+\frac{2}{10}+\frac{4}{100}+\frac{1}{1000}\] (g) \[=12+0.2+0.04+0.001=12.241\] (h) \[0.29=0+\frac{2}{10}+\frac{9}{100}\] (i) \[2.08=2+\frac{0}{10}+\frac{8}{100}\] (j) \[19.60=10+9+\frac{6}{10}+\frac{0}{100}\] (k) \[14.8.32=100+40+8+\frac{3}{10}+\frac{2}{100}\]

Answer:

(a) We have, \[200.8.12=200+00+0+\frac{8}{10}+\frac{1}{100}+\frac{2}{1000}\] Here, it has 5 tenths. i.e. \[20+9+\frac{4}{10}+\frac{1}{100}\] (b) We have, \[3+\frac{7}{10}\] Here, it has 3 ones and 7 tenths. i.e. \[\frac{7}{10}+\frac{6}{100}+\frac{4}{1000}\] (c) We have, \[23+\frac{2}{10}+\frac{6}{1000}\] Here, it has 2 hundreds, 6 tens, 5 ones and one-tenths. i.e. \[700+20+5+\frac{9}{100}\] \[20+9+9+\frac{4}{10}+\frac{1}{100}=29+4\times \frac{1}{10}+1\times \frac{1}{100}\] (d) We have, \[=29+0.4+0.01=29.41\] Here, it has 7 tens, 0 ones and 8 tenths. i.e. \[137+\frac{5}{100}\](e) We have\[=137+0\times \frac{1}{10}+5\times \frac{1}{100}=137+0+0.05=137.05\] Here, it has 8 ones and 8 tenths. i.e. \[\frac{7}{10}+\frac{6}{100}+\frac{4}{1000}\] (f) We have, \[=7\times \frac{1}{10}+6\times \frac{1}{100}+4\times \frac{1}{1000}\] Here, it has only 2 tenths. i.e. \[=0.7+0.06+0.004=0.764\] (g) We have, \[23+\frac{2}{10}+\frac{6}{1000}=23+2\times \frac{1}{10}+0\times \frac{1}{100}+6\times \frac{1}{1000}\] Here, it has one ones but tenths is not complete. On multiplying by 5 in its numerator and denominator of\[=23+0.2+0+0.006=23.206\]we get \[700+20+5+\frac{9}{100}\] Here, it has 1 ones and 5 tenths. i.e. \[=725+0\times \frac{1}{10}+9\times \frac{1}{100}=725+0+0.09=725.09\] (h) We have, \[0.60=\frac{60}{100}=\frac{60\div 20}{100\div 20}=\frac{3}{5}\] To make this fraction in tenths, we have to multiply by 2 in its numerator and denominator both. \[\because \] \[0.05=\frac{5}{100}=\frac{5\div 5}{100\div 5}=\frac{1}{20}\] Here, it has 4 tenths. i.e. \[\because \] (i) We have, \[0.75=\frac{75}{100}=\frac{75\div 25}{100\div 25}=\frac{3}{4}\] To make this fraction in tenths, we have to multiply by 2 in its numerator and denominator both. \[\because \] \[0.18=\frac{18}{100}=\frac{18\div 2}{100\div 2}=\frac{3}{4}\] Here, it has 2 ones and 4 tenths. i.e. \[\because \] (j) We have, \[0.25=\frac{25}{100}=\frac{25\div 25}{100\div 25}=\frac{1}{4}\] To make this fraction in tenths, we have to multiply by 2 in its numerator and denominator of 3/5. \[\because \] \[0.125=\frac{125}{1000}=\frac{125\div 125}{1000\div 125}=\frac{1}{8}\] Here, it has 3 ones and 6 tenths. i.e. \[\because \] (k) We have, \[0.066=\frac{66}{1000}=\frac{66\div 2}{1000\div 2}=\frac{33}{500}\] To make this fraction in tenths, we have to multiply by 5 in its numerator and denominator of 1/2. \[\because \] \[\therefore \] Here, it has 4 ones and 5 tenths. i.e. \[4\times 1+5\times \frac{1}{10}=4+\frac{5}{10}=4+0.5=4.5\]