**Exercise 3.3**

*Q1. Divide: *

*(i) 142.45 by 10 *

Shifting the decimal point by one place to the left

\(\frac{142.45}{10}\)

=14.245

*(ii) 54.25 by 10*

Shifting the decimal point by one place to the left

\(\frac{54.25}{10}\)

=5.425

*(iii) 3.45 by 10*

Shifting the decimal point by one place to the left

\(\frac{3.45}{10}\)

0.345

*(iv) 0.57 by 10*

Shifting the decimal point by one place to the left

\(\frac{0.57}{10}\)

=0.057

* *

*(v) 0.043 by 10 *

Shifting the decimal point by one place to the left

\(\frac{0.043}{10}\)

=0.0043

* *

*(vi) 0.004 by 10 *

Shifting the decimal point by one place to the left

\(\frac{0.004}{10}\)

=0.0004

* *

*Q2. Divide: *

*(i) 459.5 by 100 *

Shifting the decimal point by two places to the left

\(\frac{459.5}{100}\)

=4.595

*(ii) 74.3 by 100*

Shifting the decimal point by two places to the left

\(\frac{74.3}{100}\)

=0.743

* *

*(iii) 5.8 by 100*

Shifting the decimal point by two places to the left

\(\frac{5.8}{100}\)

=0.058

* *

*(iv) 0.7 by 100*

Shifting the decimal point by two places to the left

\(\frac{0.7}{100}\)

=0.007

* *

*(v) 0.48 by 100 *

Shifting the decimal point by two places to the left

\(\frac{0.48}{100}\)

=0.0048

* *

*(vi) 0.03 by 100 *

Shifting the decimal point by two places to the left

\(\frac{0.03}{100}\)

=0.0003

* *

*Q3. Divide: *

*(i) 235.41 by 1000 *

Shifting the decimal point by three places to the left

\(\frac{235.41}{1000}\)

=0.23541

* *

*(ii) 29.5 by 1000*

Shifting the decimal point by three places to the left

\(\frac{29.5}{1000}\)

=0.0295

* *

*(iii) 3.8 by 1000*

Shifting the decimal point by three places to the left

\(\frac{3.8}{1000}\)

=0.0038

* *

*(iv) 0.7 by 1000 *

Shifting the decimal point by three places to the left

\(\frac{0.7}{1000}\)

=0.007

* *

*Q4. Divide: *

*(i) 0.45 by 9*

=\(\frac{0.45}{9}\)

=0.05

*(ii) 217.44 by 18*

=\(\frac{217.44}{18}\)

=12.08

*(iii) 319.2 by 2.28*

=\(\frac{319.2}{2.28}\)

=\(\frac{319.2\times100}{2.28\times100}\)

=\(\frac{319.2}{2.28}\)

*(iv) 40.32 by 9.6 *

=\(\frac{40.32}{9.6}\)

=\(\frac{40.32\times10}{9.6\times10}\)

=\(\frac{403.2}{96}\)

=4.2

* **(v) 0.765 by 0.9 *

=\(\frac{0.765}{0.9}\)

=\(\frac{0.765\times10}{0.9\times10}\)

=\(\frac{7.65}{9}\)

=0.85

* *

* *

*(vi) 0.768 by 1.6*

=\(\frac{0.768}{1.6}\)

=\(\frac{0.768\times10}{1.6\times10}\)

=\(\frac{7.68}{16}\)

=0.48

* *

*Q5. Divide: *

*(i) 16.64 by 20 *

=\(\frac{16.64}{20}\)

=\(\frac{16.64}{2\times10}\)

=\(\frac{16.64}{10}\times\frac{1}{2}\)

=\(\frac{1.664}{2}\)

=0.832

* *

*(ii) 0.192 by 12*

=\(\frac{0.192}{12}\)

=0.016

* *

*(iii) 163.44 by 24 *

=\(\frac{0.192}{12}\)

=6.81

*(iv) 403.2 by 96*

=\(\frac{403.2}{96}\)

=4.2

* *

* **(v) 16.344 by 12 *

=\(\frac{16.344}{12}\)

=1.362

* *

*(vi) 31.92 by 228*

=\(\frac{31.92}{228}\)

=0.14

* *

*Q6. Divide: *

*(i) 15.68 by 20 *

=\(\frac{15.68}{20}\)

=\(\frac{15.68}{2\times10}\)

=\(\frac{15.68}{10}\times\frac{1}{2}\)

=\(\frac{1.568}{2}\)

=0.784

* *

* (ii) 164.6 by 200 *

=\(\frac{164.6}{200}\)

=\(\frac{164.6}{2\times100}\)

=\(\frac{164.6}{100}\times\frac{1}{2}\)

=\(\frac{1.646}{2}\)

=0.823

* *

*(iii) 403.80 by 30*

=\(\frac{403.80}{30}\)

=\(\frac{403.80}{3\times10}\)

=\(\frac{403.80}{10}\times\frac{1}{3}\)

=\(\frac{40.380}{3}\)

=13.46

*Q7. Divide: *

*(i) 76 by 0.019 *

=\(\frac{76}{0.019}\)

=\(\frac{76\times1000}{0.019\times1000}\)

=\(\frac{76000}{19}\)

=4000

*(ii) 88 by 0.08 *

=\(\frac{88}{0.08}\)

=\(\frac{88\times100}{0.08\times100}\)

=\(\frac{8800}{8}\)

=1100

* *

*(iii) 148 by 0.074 *

=\(\frac{148}{0.074}\)

=\(\frac{148\times1000}{0.074\times1000}\)

=\(\frac{148000}{74}\)

=2000

*(iv) 7 by 0.014 *

=\(\frac{7}{0.014}\)

=\(\frac{7\times1000}{0.014\times1000}\)

=\(\frac{7000}{14}\)

* *

*Q8. Divide: *

*(i) 20 by 50 *

=\(\frac{20}{50}\)

* *

*(ii) 8 by 100 *

=\(\frac{8}{100}\)

By shifting the decimal point to the left

=\(\frac{8}{100}\)

=0.08

*(iii) 72 by 576 *

=\(\frac{72}{576}\)

=0.125

* *

*(iv) 144 by 15 *

=\(\frac{144}{15}\)

* *

=9.6

* *

*Q9. A vehicle covers a distance of 43.2 km in 2.4 litres of petrol. How much distance will it travel in 1 litre of petrol? *

Distance covered in 2.4 litres of petrol=43.2km

Distance covered in 1 litre of petrol= \(\frac{43.2}{2.4}\)

=18km

The distance travelled in 1 litre of petrol is 18 km

*Q10. The total weight of some bags of wheat is 1743 kg. If each bag weights 49.8 kg, how many bags are there? *

Total weight of bags of wheat=1743kg

Each bag weight=49.8kg

No of bags= \(\frac{1743}{49.8}\)

=\(\frac{1743\times10}{49.8\times10}\)

=\(\frac{17430}{498}\)

=34

Therefore the total numbers of bags are 35

*Q11. Shikha cuts 50 m of cloth into pieces of 1.25 m each. How many pieces does she get? *

Total length of cloth= 50m

Length of each piece of cloth=1.25m

Number of pieces=\(\frac{50}{1.25}\)

=\(\frac{50\times100}{1.25\times100}\)

=\(\frac{5000}{125}\)

=40 pieces

Therefore Shikha got 40 pieces

*Q12. Each side of a rectangular polygon is 2.5 cm in length. The perimeter of the polygon is 12.5 cm. How many sides does the polygon have? *

Length of each side of rectangular polygon=5.2cm

Perimeter of polygon=12.5cm

No of sides polygon has=12.5cm

No of sides polygon have=\(\frac{12.5}{2.5}\)

=\(\frac{12.5\times10}{2.5\times10}\)

=5

Therefore the sides of the polygon is 5

*Q13. The product of two decimals is 42.987. If one of them is 12.46, find the other. *

We have,

The product of the given decimals=42.987

` one decimal=12.46

The other decimal=\(\frac{42.987}{12.46}\)

=3.45

The number is 3.45

*Q14. The weight of 34 bags of sugar is 3483.3 kg. If all bags weigh equally, find the weight of each bag. *

Total weight of sugar= 3483.3kg

No of bags= 34

Weight of each bag=\(\frac{3483.3}{34}\)

=102.45kg

Therefore weight of each bag is 102.45kg

*Q15. How many buckets of equal capacity can be filled from 586.5 litres of water, if each bucket has capacity of 8.5 litres?*

Capacity of each bucket=805 litres

Total water available=586.5litres

Number of buckets=\(\frac{805}{586.5}\)

=\(\frac{805\times10}{586.5\times10}\)

=69

Total number of buckets is 69