EXERCISE 2.6
Question 1
\text { i) } 2.7 \times 4=\frac{27}{10} \times 4
$=\frac{108}{10}=10.8$
ii) $2.71 \times 5=\frac{271}{100} \times 5$
$=\frac{1355}{100}=13.55 .$
iii) $2.5 \times 0.3=\frac{25}{10} \times \frac{3}{10}$
$=\frac{75}{100}=0.75$
iv)$2.3 \times 4.35=\frac{23}{10} \times \frac{435}{100}$
$=\frac{10005}{1000}=10: 005$
v) $238.06 \times 7.5=\frac{23806}{100} \times \frac{75}{10}=\frac{1785450}{1000}=1785.45 .$
vi)$0.79 \times 32.4=\frac{79}{100} \times \frac{324}{10}=\frac{25,596}{1000}=25.596$
vii) $1.07 \times 0.02=\frac{107}{100} \times \frac{2}{100}=\frac{214}{10000}=0.0214 .$
viii) $10.05 \times 1.05=\frac{1005}{100} \times \frac{105}{100}=\frac{105.525}{10000}=10.5525$
Question 2
i) (diagram to be added)
= 2.7
ii) $126.35 \div 7$
(diagram to be added)
Ans = 18.05
iii) $22.5 \div 1.5=\frac{22.5}{1.5} \times \frac{10}{10}=\frac{225}{15}$
(diagram to be added)
Hence, $22.5 \div 1.5=15$.
iv) $4 \cdot 28 \div 0.02=\frac{4.28}{0.02} \times \frac{100}{100}=\frac{428}{2}$
(diagram to be added)
Hence, $4.28 \div 0.02=214$.
v)$3.645 \div 1.35=\frac{3.645}{1.350} \times \frac{1000}{1000}=\frac{3645}{1350}$
(diagram to be added)
Hence, $3.645 \div 1.35=2.7$
vi)$0.728 \div 0.04=\frac{0.728}{0.040} \times \frac{1000}{1000}=\frac{782}{40}$
$=\frac{182}{10}$
$=18.2$
vii)$13.06 \div 0.08=\frac{13.01}{0.08} \times \frac{100}{100}=\frac{1306}{8}$
(diagram to be added)
Hence, $13.06 \div 0.08=163.25$.
viii)$58.635 \div 4.5=\frac{58.635}{4.500} \times \frac{1000}{1000}=\frac{58635}{4500}$
(diagram to be added)
Hence, $58.635 \div 4.5=13.03$
Question 3
i) $5.9 \times 10=59$
$5.9 \times 100=590$
$5.9 \times 1000=5900$
To Multiply by 10, shift decimal point to the right by one place
ii) $3.76 \times 10=37.6$
$3.76 \times 100=376$
$3.76 \times 1000=3760$
iii) $0.549 \times 10=5.49$
$0.549 \times 100=54.9$
$0.549 \times 1000=549$
Question 4
To divide a decimals number by 10,100,1000 Shift decimal point to the left by one, two three places.
i) $4.8 \div 10=0.48 \quad 4.8 \div 1000=0.0048$
$4.8 \div 100=0.048$
ii)
$\begin{aligned} 38.53 \div 10 &=3.853 \\ 38.53 \div 100 &=0.3853 \\ 38.53 \div 1000 &=0.03853 . \end{aligned}$
iii) $128.9 \div 10=12.89$
$128.9 \div 100=1.289$
$128.9 \div 1000=0.1289$
Question 5
Given length = 5.7cm ; Breadth = 3.5cm
Area of rectangle A =Length $\times$ Breadth
$=5.3 \times 3.5$
$=\frac{57}{10} \times \frac{35}{10}$
$=\frac{1995}{100}$
$=19.95 \mathrm{Cm}^{2} .$
Question 6
Given, cost of one metre cloth is Rs 38.50
Cost of 3.6 metre cloth is $3.6 \times 38.5$
$=\frac{36}{10} \times \frac{355}{10}$
$=\frac{13860}{100}$
$=₹ 138.60$
Question 7
One liter of petrol covers distance $=45.3 \mathrm{~km}$
$5.9$ litres of petrol covers distance $=5.9 \times 45.3 \mathrm{~km}$
$=\frac{59}{10} \times \frac{453}{10} \mathrm{~km}$
$=\frac{26727}{100} \mathrm{~km}$
$=267.27 \mathrm{~km}$
Question 8
$1 \mathrm{~kg}$ of pure milk contains $=0.245 \mathrm{kg}$ fat
$12.8 \mathrm{~kg}$ of milk contains $=12.8 \times 0.245$'
=$\frac{128}{10} \times \frac{245}{1000}$
=$\frac{31360}{10000}$
=$3.136 \mathrm{~kg}$
Question 9
6 Children Shared equally
Total rupees wik them ar $\overline{2} 242 \cdot 46$.
Then each Childred shared $=5 \frac{242.46}{6}$
$=\frac{\left(\frac{24246}{100}\right)}{6}$
$= \frac{24246}{100 \times 6}$
$= \frac{4041}{100}$
Rs $40.41$
∴ Each Children shared Rs 40.41
Question 10
$2.4$ litres of petrol coress a distance $=43.2 \mathrm{~km}$
one litre of petrol Covers a distance $=\frac{43.2}{2 \cdot 4} \mathrm{~km}$
$=\frac{432 / 10}{24 / 10}$
$=\frac{432}{10} \times \frac{10}{24}$
$=\frac{432}{24}$
=18km
Question 11
Total 8.4 litres of icecream
One cone can be filled with 35 millilitres of icecream
Number of icecream cones can be filled
$=\frac{8.4 \times 1000 \mathrm{ml}}{35 \mathrm0{ml}}$ (As 1 litre = 1000ml)
$=\frac{8400}{35}$
Number of icecream cones = 240
Question 12
Product of two decimal numbers = 38.745
One of the number is 2.7
Let the other number be x
i.e $x \times 2.7=38.745$
$-x=\frac{38.745}{2.7}$
$x=\frac{38745 / 1000}{27 / 10}$
$x=\frac{38745}{1000} \times \frac{10}{27}$
$x=\frac{1435}{100}$
$x=14.75$
The other number is 14.35
Question 13
Let the number be 'x'
Given $\frac{2}{3}$ of a number is 10
$\begin{aligned} \frac{2}{3} \times x &=10 \\ x &=\frac{50 \times 3}{2} \\ x &=15 \end{aligned}$
The number x = 15
∴ Now 1.75 times of number = $=1.75 \times 15$
$=\frac{135}{100} \times 15$
$=\frac{2625}{100}$
=26.25
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