EXERCISE:2.5
Question 1
i) $20.03=2 \times 10+0 \times 1+0 \times \frac{1}{10}+3 \times \frac{1}{100}$
ii) $200.03=2 \times 100+0 \times 10+0 \times 1+0 \times \frac{1}{10}+3 \times \frac{1}{100}$
iii) $2.034=2 \times 1+0 \times \frac{1}{10}+3 \times \frac{1}{100}+4 \times \frac{1}{1000}$.
Question 2
i) Place value of digit 2 in $2.56$ is $2 \times 1=2$
ii) place value of digit 2 in $21.37$ is $2 \times 10=20$
iii) place value of digit 2 in $10.25$ is $2 \times \frac{1}{10}=\frac{2}{10}$.
iv) place Value of digit 2 in $63 \cdot 352$ is $2 \times \frac{1}{1000}=\frac{2}{1000}$.
Question 3
i) $0.8=\frac{8}{10}=\frac{4}{5}$
ii) $0.225=\frac{225}{1000}=\frac{9}{40}$
iii) $0.0092=\frac{92}{10000}=\frac{23}{2500}$
iv) $3.025=\frac{3025}{1000}=\frac{121}{40}$
Question 4
i) $5.05=\frac{505}{100}=5+\frac{5}{100}=5+\frac{1}{20}=5 \frac{1}{20}$
ii) $63.125=63+\frac{125}{1000}=63+\frac{1}{8}=63 \frac{1}{8}$
iii) $17.075=17+\frac{75}{1000}=17+\frac{3}{40}=17 \frac{3}{40}$.
iv) $317.0006=312+\frac{6}{10000}=317+\frac{3}{5000} = 317 \frac{3}{5000}$
Question 5
i) $\frac{3}{5}=\frac{3 \times 2}{5 \times 2}=\frac{6}{10}=0.6$
ii) $\frac{7}{8}=\frac{7 \times 125}{8 \times 125}=\frac{875}{1000}=0.875$
iii) $3 \frac{5}{16}=\frac{3 \times 16 \p 5}{16}=\frac{53}{16}=\frac{53 \times 625}{16 \times 10000}=\frac{33125}{10000}=3.3125$
iv) $137 \frac{13}{625}=137+\frac{13}{625}=137+\frac{13 \times 16}{625 \times 16}=137+\frac{208}{10000}$
$=137+0.0208$
$=137.0208$
Question 6
(i) 0.5 or 0.05 are like decimal mumbers
We know that whole number parts of given number are equal
Let us their digits at tenth place
In both number , digits at tenth place in 0.5 is 5 and digits at tenth place in 0.05 is 0
Since $5>0$, So 0.5 $>0.05 .$
(ii)Given numbers are 7,0.7
Whole numbers parts of given numbers are not equal
In number 7 , the whole number is 7
In number $0.7$, the whole number is 0 .
since $7>0$, so $7>0.7$
(iii) Given numbers are 2.03 or 2.30
We note that whole number parts of given number are equal
Let us compare their tenth digits
In 2.03 digits at tenth place is 0
In 2.30 digits at tenth place is 3
Since $3>0$, so $2.30>2.03$
(iv) Given numbers are 0.80 or 0.88
We know that whole number parts of given number are equal
Let us compare their tenth digits
In both number , digits at tenth place = 8
So, we compare their hundreth place
In 0.80 digits at hundreth place = 0
In 0.88 , digits at hundredth place = 8
Since $8>0$, so $0.88>0.80$.
Question 7
(i) Compare whole numbers
$83>38>3 \quad$ (or) $\quad 3<38<83$
Compare tenth digits numbers in $38,02,38 \cdot 021,38.002$
In $38.02$, the tenth digit is 0
In $38.021,38.002$, the tenth digit is 0
Compare hundredth digits
In $38.02,38.021$, he hundred th digit is 2
But In $38.002$, the hundred th digit is 0
$\quad since \quad 0<2, \quad 38 \cdot 002<(38.02,38\cdot 021)$
Compare thousandth's place in 38.020, 38.021
In 38 .020 the thousandth place is 0
In 38.021 the thousandth place is 1
Since $0<1$, So $38.020<38.021$
∴ So the ascending order is $3.802<38.002<38.420<38.21$
$<83: 02$
(ii) In all the given numbers except $64.542$, all are having
46 as their whele number.
So $64.542$ is the highest $(m)$ largest number
Comparing tenth digits
In $46.542$, the tenth digit is 5
In $46.452$, the tenth digit is 4
In $46.254$, the tenth digh is 2
Since $2<4<5$, so $46.254<46.452<46542$
Compare hundredth and thousand place in 46.05, 46.0542
In both numbers hundredth and tenth digits is same 5,0
In 46.050,the thousandth digit is 0
In 46.0542, the thousandth digits is 4
Since $0<4$, so $46.050<46.0542$
∴ Ascending order is $46.050<46.0542<46.254<46.452<46.542<64.542$
Question 8
(i) We know that $5>1>0$. (whole numbers)
Now $1.87,1.9,1.78$
The tenth digit are 8 , 9 , 7
Since $9>8>7$, so $1.9>1.87>1.78$
Now In 0.93, 0.39
The tenth digits are 9, 3
Since $9>3$, so $0.93>0.39$
∴ Descending order is $5.6>1.9>1.87>1.78>0.93>0.39$
(ii) We know that $71 \geqslant 20>3>2>0$ in whole number
Compare Tenth digits in $2.01,2.14$
In $2.01$, The tenth digit is 0
In $2.14$, the tenth digit is 1
since $1>0$, so $2.14>2.01$
∴ Descending order is $71.201>20.1>3.1>2.14>2.01>0.652$
Question 9
(i)
$\begin{aligned} 1 \text { Rupee } &=100 \text { paise } \\ \text { So } 1 \text { paise } &=\frac{1}{100} \text { rupee } \end{aligned}$
$\begin{aligned} 7 \text { paise }=7 \times \frac{1}{100} \text { rupee } &=\frac{7}{160} \text { rypee } \\ &=0.07 \text { rupee } \end{aligned}$
(ii) 77 rupees 77 paise
$=\left[77+77 \times \frac{1}{100}\right] \mathrm{rupee}$
$=\left[77+\frac{77}{100}\right]$ rupee
$=[27+0.77]$ ruper
$=77.77$ rupee
(iii) 235 paise $=235 \times \frac{1}{100}$ rupes $=$ 2.35. rupee
Question 10
We know 1m =100cm $\Rightarrow k m=\frac{1}{100} m$
$1 \mathrm{~km}=1000 \mathrm{~m} \Rightarrow \mathrm{1m}=\frac{1}{1000} \mathrm{~km}$
5cm =$5 \times \frac{1}{100} m=0.05 \mathrm{~m}$
$0.05 m=\frac{5}{100} m=\frac{5}{100} \times \frac{1}{1000} km=0.00005 \mathrm{~km}$\
Question 11
We know 1kg =100g
So $\quad 1 g=\frac{1}{1000} k_{g}$
i) $200 g=200 \times \frac{1}{1000} k_{g}=\frac{2}{10} k_{9}=0.2 \mathrm{~kg}$
ii) $3470 g=347 \times \times \frac{1}{1000} k_{9}=\frac{347}{100} \mathrm{~kg}=3.47 \mathrm{~kg}$
iii)$4 \mathrm{~kg} 8 \mathrm{~g}= \left(4+\frac{8}{1000}\right) \mathrm{kg}=(4+0.008) \mathrm{kg}=4.008 \mathrm{~kg}$
Question 12
i) $S u m=5.765+9.2+3.08$
$\begin{array}{r}5.765 \\+9.200 \\+3.080 \\\hline 18.045\end{array}$
(ii) $\begin{array}{r}15.4900 \\+8.3572 \\+0.9030 \\+\quad 7.8000 \\\hline 32.5502\end{array}$
Question 13
(i)
$\begin{array}{r}72.530 \\-\quad 46.782 \\\hline 25.748\end{array}$
(ii)Given the positive and negative numbers seperately
Positive numbers Negative numbers
18.376 $\begin{array}{r}5.4300 \\+8.8976 \\\hline 14.3276\end{array}$
$\begin{array}{r}18.3760 \\-14.3276 \\\hline4.0484\end{array}$
(iii) positive number
28. 5
$\begin{array}{l}\text { Negative number } \\9.708 \\+6.234 \\\hline 15.942\end{array}$
$\begin{array}{r}28.500 \\-15.942 \\\hline=12.558\end{array}$
(iv) Positive numbers
$\begin{array}{l}8.20 \\2.67 \\\hline 10.87\end{array}$
Negative numbers
$\begin{array}{r}4.5600 \\+0.7912 \\\hline 5.3512\end{array}$
$\begin{array}{r}10.8700 \\-5.3512 \\\hline5.5188\end{array}$
Question 14
i) Let the number added = x
$\begin{aligned} x+3.56 &=13.016 \\ x &=13.016-3.56 \end{aligned}$
$\begin{array}{r}13.016 \\-3.560 \\\hline 9.456\end{array}$
x = 9.456
(ii) Let the number Substracted be x
$\begin{aligned} 30-x &=23.709 \\ x &=30-23.709 \end{aligned}$
$\begin{array}{r}30.000 \\-23.709 \\\hline 6.291\end{array}$
x=6.291
(iii) Excess of 20.4 over 9.7403 is
= 20.4-9.7403
$\begin{array}{r}20.4000 \\-9.4403 \\\hline 10.6597\end{array}$
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