Exercise 1

Convert each measurement to meters.

13 km 5 hm 7 dam

27 m 4 cm 3 mm

325.56 dam + 526.9 dm

453,600 mm + 9,830 cm

51.83 hm + 9.7 dam + 3,700 cm

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Exercise 2

Convert each measurement to liters:

13 kl 5 hl 7 dal

27 l 4 cl 3 ml

325.56 dal + 526.9 dl

453,600 ml + 9,830 cl

51.83 hl + 9.7 dal + 3,700 cl

Exercise 3

Convert each measurement to grams:

15 kg 3 hg 4 g

24 hg 8 dag 2 g 5 dg

32 dag 3 g 8 dg 7 cg

435 dg 480 cg 2,600 mg

Exercise 4

Convert each measurement to centiliters:

1 3 dal 7l 5 dl 4 cl 5 ml

2 6 hl 8 l 2 ml

3 0.072 kl + 5.06 dal + 400 ml

4 0.000534 kl + 0.47 l

Exercise 5

Convert each measurement to centigrams:

1 3 dag 7 g 5 dg 4 cg 5 mg

2 6 hg 8 g 2 mg

3 0.072 kg + 5.06 dag + 400 mg

4 0.000534 kg + 0.47 g

Exercise 6

Convert each measurement to meters:

15 km 3 hm 4 m

24 hm 8 dam 2 m 5 dm

32 dam 3 m 8 dm 7 cm

435 dm 480 cm 2,600 mm

Exercise 7

Mariah bought 4.8 kg of flour. Her brother John is baking a cake and she gives \frac{1}{8} th of the flour to him. How much flour is left with Mariah in milligrams?

Exercise 8

The maximum water that can be stored in a well is 80 dal. There is another smaller well that can store only 40% as much water as the bigger well can store. How much more water in liters can the bigger well store than the smaller well?

Example 9

George wants to start jogging from the next week to improve his fitness. There are two jogging tracks. The length of the first jogging track is 4140 meters and the length of the second track is 2800 m 15 hm 15 dam. George wants to choose the longest track for jogging. What is the length of the longest track in kilometers?

Example 10

The garden of the mansion spreads on 1/4 of the area of the entire house. The total area of the mansion is 84 Ares . What is the land in meter squares that is covered by the garden and the mansion?

 

Solution of exercise 1

Convert each measurement to meters:

13 km 5 hm 7 dam 3,000 m + 500 m + 70 m = 3,570 m

27 m 4 cm 3 mm 7 m + 0.04 m + 0.003 m = 7.043 m

325.56 dam + 526.9 dm 255.6 m + 52.69 m = 308.29 m

453,600 mm + 9,830 cm 53.6 m + 98.3 m = 151.9 m

51.83 hm + 9.7 dam + 3,700 cm 183 m + 97 m + 37 m = 317 m

 

Solution of exercise 2

Convert each measurement to liters:

13 kl 5 hl 7 dal 3,000 l + 500 l + 70 l = 3,570 l

27 l 4 cl 3 ml 7 l + 0.04 l + 0.003 l = 7.043 l

325.56 dal + 526.9 dl 255.6 l + 52.69 l = 308.29 l

453,600 ml + 9,830 cl 53.6 l + 98.3 l = 151.9 l

51.83 hl + 9.7 dal + 3,700 cl 183 l + 97 l + 37 l = 317 l

 

Solution of exercise 3

Convert each measurement to grams:

15 kg 3 hg 4 g 5,000 g + 300 g + 4 g = 5,304 g

24 hg 8 dag 2 g 5 dg 400 g + 80 g + 2 g + 0.5 g = 482.5 g

32 dag 3 g 8 dg 7 cg 20 g + 3 g + 0.8 g + 0.07 g = 23.87 g

435 dg 480 cg 2,600 mg 3.5 g + 4.8 g + 2.6 g = 10.9 g

 

Solution of exercise 4

Convert each measurement to centiliters:

13 dal 7l 5 dl 4 cl 5 ml

3,000 cl + 700 cl + 50 cl + 4 cl + 0.5 cl = 3,754.5 cl

26 hl 8 l 2 ml

60,000 cl + 800 cl + 0.2 cl= 60,800.2 cl

30.072 kl + 5.06 dal + 400 ml

7,200 cl + 5,060 cl + 40 cl = 12,300 cl

4 0.000534 kl + 0.47 l

53.4 cl + 47 cl = 100.4 cl

 

Solution of exercise 5

Convert each measurement to centigrams:

13 dag 7 g 5 dg 4 cg 5 mg

3,000 cg + 700 cg + 50 cg + 4 cg + 0.5 cg = 3,754.5 cg

26 hg 8 g 2 mg

60,000 cg + 800 cg + 0.2 cg = 60,800.2 cg

30.072 kg + 5.06 dag + 400 mg

7,200 cg + 5,060 cg + 40 cg = 12,300 cg

 

Solution of exercise 6

Convert each measurement to meters:

15 km 3 hm 4 m 5,000 m + 300 m + 4 m = 5,304 m

24 hm 8 dam 2 m 5 dm 400 m + 80 m+ 2 m + 0.5 m = 482.5 m

32 dam 3 m 8 dm 7 cm 20 m+ 3 m + 0.8 m + 0.07 m = 23.87 m

435 dm 480 cm 2,600 mm 3.5 m + 4.8 m + 2.6 m = 10.9 m

 

Solution of exercise 7

First, we will find out the amount of flour in milligrams that was given to John.

The total amount of flour Mariah had = 16 kg

Amount she gave to her brother = \frac{1} {8} \cdot 4.8 = 0.6 kg

Amount of flour left = 4.8 - 0.6 = 4.2 kg

Now, we will convert the kilograms into grams and then the resulting grams will be converted into milligrams.

1 kilogram = 1000 grams

4.2 kg = 4.2 x 1000 = 4800 grams

1 gram = 1000 milligrams

4800 grams = 4800 x 1000 = 4800,000 milligrams

Hence, Mariah had 4800,000 mg of flour left after giving \frac{1}{8} th to her brother.

 

Solution of exercise 8

We need to determine the extra amount of water in liters that can be stored in a bigger well.

The capacity of the bigger well = 80 dal

The capacity of the smaller well = \frac{40}{100} \cdot 80 = 32 dal

Extra amount of water that can be stored in a bigger well = 80 - 32 = 48 dal

Now, we will convert decaliters into liters.

1 dal = 10 liters

48 dal = 48 x 10 liters

= 480 liters

Hence, the bigger well can store 480 liters more water than the smaller well.

 

Solution of exercise 9

Length of the first jogging track = 4140 m

1 km = 1000 m

4140 m = \frac{4140}{1000} m

= 4.140 km

Hence, the length of the first jogging track in kilometers = 4.140 km

 

Length of the second jogging track = 2800 m 15 hm 15 dm

Since the length of the second track is given as a complex measurement, therefore, we will convert it into a simple measurement to determine the length of the longest track in kilometers.

1 km = 1000 m

2800 m = \frac{2800}{1000} m

= 2.8 km

1 hm = 100 m

15 hm = 15 x 100

= 1500 m

= \frac{1500}{1000} km

= 1.5 km

1 dam = 10 m

15 dam = 15 x 10 = 150 m

= \frac{150}{1000} km

= 0.15 km

Length of the second track = 2.8 + 1.5 + 0.15 = 4.45 km

The length of the first track is 4.14 km and the length of the second track is 4.45 kilometers. Hence, the second track has more length than the first track.

 

Solution of exercise 10

Total area of the mansion = 84 Ares

The area of the garden = \frac{1}{4} \cdot 84 = 21 Ares

Now, we will convert Ares into meter squares.

1 Are = 100 m^2

21 Ares = 2100 m^2

Hence, the maximum area of the land that is covered by the garden is 2100 m^2.

Now, we will find out the area covered by the mansion itself.

Area covered by mansion = Total area - Area covered by garden

= 84 - 21

= 63 Ares

Area of the mansion in m^2 = 63 x 100

= 6300 m^2

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.