question_answer 18)

Which is greater? (a) 0.3 or 0.4 (b) 0.07 or 0.02 (c) 3 or 0.8 (d) 0.5 or 0.05 (e) 1.23 or 1.2 (f) 0.099 or 0.19 (g) 1.5 or 1.50 (h) 1.431 or 1.490 (i) 3.3 or 3.300 (j) 5.64 or 5.603 TIPS Firstly, write the given decimal in place value term to know about greater in given two decimals. We first compare the whole part and decimal having greater whole part will be greater. If whole part is same for both, then compare the tenths part and decimal having greater tenths part will be greater. If tenths part is also same, then compare the hundredths part and decimal having greater hundredths part will be greater. If hundredths part is same, then compare the thousandths part and find greater decimal number.

Answer:

(a) We have, 0.3 or 0.4 \[\frac{1}{100}.\] \[\therefore \] and \[1cm=\frac{1}{100}m=0.01m\] Here, whole part of both numbers are same. Now, tenths part of \[\therefore \] and tenths part of \[1m=\frac{1}{1000}km\] Here, 4 is greater than 3. \[\therefore \] \[1mm=\frac{1}{10}cm\] Hence, 0.4 is greater than 0.3. (b) We have, 0.07 or 0.02 \[\therefore \] \[1g=\frac{1}{1000}kg=0.001kg\] and \[\frac{1}{1000}\] Here, whole parts as well as tenths parts of both numbers are same i.e. 0. Now, hundredths part of \[\left( \frac{1}{10} \right)\] and hundredths part of \[=5\times 100+3\times 10+8\times 1+1\times \frac{1}{10}\] Here, 7 is greater than \[=500+30+8+\frac{1}{10}=538+0.1=538.1\]\[=2\times 100+7\times 10+3\times 1+4\times \frac{1}{10}\] Hence, 0.07 is greater than 6.02. (c) We have, 3 or 0.8 \[=200+70+3+\frac{4}{10}=273+0.4=273.4\] \[=3\times 100+5\times 10+4\times 1+6\times \frac{1}{10}\] and \[=300+50+4+\frac{6}{10}=354+0.6=354.6\] Here, whole part of number 3 = 3 and whole part of number 0.8 = 0 \[\because \] \[3>0\] Hence, 3 is greater than 0.8. (d) We have, 0.5 or 0.05 \[\therefore \]\[1mm=\frac{1}{10}cm\] and \[=7cm+\frac{5}{10}cm=7cm+0.5cm=7.5cm\] Here, whole parts of both numbers are same i.e. 0. Now, tenths part of \[=8cm+\frac{3}{10}cm=8\text{ }cm+0.3\text{ }cm=8.3\text{ }cm\]and tenths part of \[\text{2}\times \text{hundreds+1}\times \text{ten+6}\times \text{ones+3}\times \text{tenths}\] \[=2\times 100+1\times 10+6\times 1+3\times \frac{1}{10}\] \[=200+10+6+\frac{3}{10}=216+0.3=216.3\] Hence, 0.5 is greater than 0.05. (e) We have, 1.23 or 1.2 \[\text{4}\times \text{hundreds+5}\times \text{tens+4}\times \text{ones+2}\times \text{tenths}\] \[=4\times 100+5\times 10+4\times 1+2\times \frac{1}{10}\] and \[=400+50+4+\frac{2}{10}=454+0.2=454.2\] Here, whole parts and tenths parts of both numbers are same. Now, hundredths part of \[\text{7}\times \text{hundreds+3}\times \text{tens+2}\times \text{ones+1}\times \text{tenths}\] and hundredths part of \[=7\times 100+3\times 20+2\times 1+1\times \frac{1}{10}\] \[=700+30+2+\frac{1}{10}=732+0.1=732.1\] \[\frac{3}{2},\frac{4}{5}\] Hence, 1.23 is greater than 1.2. (f) We have, 0.099 or 0.19 \[\frac{8}{5}\] \[\frac{3}{2}=\frac{3\times 5}{2\times 5}\] and \[=\frac{15}{10}=1\frac{5}{10}=1+\frac{5}{10}=1+0.5=1.5\] Here, whole parts of both numbers are same. Now, tenths part of \[\frac{3}{2}\]and tenths part of \[\frac{4}{5}=\frac{4\times 2}{5\times 2}\] \[=\frac{8}{10}=0.8\] \[\frac{4}{5}\] Hence, 0.19 is greater than 0.099. (g) We have, 1.5 or 1.50 \[\frac{8}{5}=\frac{8\times 2}{5\times 2}\] \[=\frac{16}{10}=1\frac{6}{10}=1+\frac{6}{10}=1+0.6=1.6\] and \[\frac{8}{5}\] Here, whole parts, tenths parts are well as hundredths parts of both numbers are same. \[\therefore \] 1.5 = 1.50 Hence, both numbers are equal. (h) We have, 1.431 or 1.490 \[\therefore \] \[1.431=1+\frac{4}{10}+\frac{3}{100}+\frac{1}{1000}\] and \[1.490=1+\frac{4}{10}+\frac{9}{100}+\frac{0}{1000}\] here, whole parts and tenths parts of both numbers are same. Now, hundredths part of \[1.431=\frac{3}{100}\] And hundredths part of \[1.490=\frac{9}{100}\] \[\therefore \] \[\frac{9}{100}>\frac{3}{100}\] Hence, 1.490 is greater than 1.431. (i) We have, 3.3 or 3.300 \[\therefore \] \[3.3=3+\frac{3}{10}+\frac{0}{100}+\frac{0}{1000}\] and \[3.300=3+\frac{3}{10}+\frac{0}{100}+\frac{0}{1000}\] here, whole parts, tenths parts, hundredths part as well as thousandths parts of both numbers are same. \[\therefore \] 3.3 = 3.300 Hence, both numbers are equal. (j) We have, 5.64 or 5.603 \[\therefore \] \[5.64=5+\frac{6}{10}+\frac{4}{100}+\frac{0}{1000}\] and \[5.603=5+\frac{6}{10}+\frac{0}{100}+\frac{3}{1000}\] Here, whole parts and tenths parts of both numbers are same. Now, hundredths part of \[5.64=\frac{4}{100}\] and hundredths part of \[5.603=\frac{0}{100}\] \[\therefore \] \[\frac{4}{100}>\frac{0}{100}\] Hence, 5.64 is greater than 5.603.