Arithmetic Chapter 7 Matric System
Question 1.
1.
1. 1.8 metres = How many millimetres?
Solution: 1.8 metres = 1.8 x 10 decimetres
= 1.8 x 10 x 10 centimetres
= 1.8 x 10 x 10 x 10 millimetres
= 1.8 x 1000 millimetres
= 1800.0 millimeters
= 1800 millimeters.
1.8 metres = 1800 millimeters.
2. 3 metres 17 cm = How many cm ?
Solution: 3 metres 17 cm = 3 x 10 decimetres + 17 cm
= 3 x 10 x 10 cm + 17 cm
= 300 cm + 17 cm ;
= 317 cm
3 metres 17 cm = 317 cm
Read and Learn More WBBSE Solutions For Class 6 Maths
3. 2.356 metres = How many decimetres?
Solution: 2.356 metres = 2.356 x 10 decimetres
= 23.56 decimetres.
2.356 metres = 23.56 decimetres.
4. 5.37 hectometres = How many decametres?
Solution: 5.37 hectometres = 5.37 x 10 decametres
= 53.7 decametres.
5.37 hectometres = 53.7 decametres.
WBBSE Class 6 Metric System Notes
5. 6 decametres 7 decimetres = How many decimetres ?
Solution: 6 decametres 7 decimetres = 6 x 10 metres + 7 decimetres
= 6 x 10 x 10 decimetres + 7 decimetres
= 600 decimetres + 7 decimetres
= 607 decimetres.
6 decametres 7 decimetres = 607 decimetres.
6. 0.2 cm = How many metres?
Solution: 0.2 cm = (0.2 ÷ 10) decimetre
= {(0.2 ÷ 10) 10} metre .
= {0.02 ÷ 10} metre
= 0.002 meters.
0.2 cm = 0.002 meters.
7. 5 metres = How many decametres?
Solution: 5 meters = (5 ÷ 10) decametre.
= 0.5 decametres.
5 meters = 0.5 decametres.
Short Questions on Metric Measurements
8. 5.3 cm = How many decametres?
Solution: 5.3 cm = (5.3 ÷ 10) decimeter
= {(5.3 ÷ 10) ÷ 10} metre
= {0.53 ÷ 10} metre
= 0.053 meter
= (0.053 ÷ 10) decametre
= 0.0053 decametre.
5.3 cm = 0.0053 decametre.
9. 0.7 decametre = How many kilometres?
Solution: 0.7 decametre = (0.7 ÷ 10) hectometer
= 0.07 hectometres
= (0.07 ÷ 10) kilometre
= 0.007 kilometers.
0.7 decametre = 0.007 kilometers.
10. 91 meters = How many kilometers?
Solution: 91 metres = (91 ÷ 10) decametres
= 9.1 decametres
= 91 ÷ 10 hectometres
= 0.91 hectometre
= (0.91 ÷ 10) kilometre
= 0.091 kilometers.
91 metres = 0.091 kilometers.
2.
Common Questions About Metric Units
1. 2 kilograms = How many hectograms?
Solution: 2 kilograms = 2 x 10 hectograms
= 20 hectograms
2 kilograms = 20 hectograms
2. 500 grams = How many kilograms?
Solution: 500 grams = (500 ÷ 10) decagrams
= 50 decagrams
= (50 ÷ 10) hectograms
= 5 hectograms
= (5 ÷ 10) kilograms
= 0.5 kilograms
500 grams = 0.5 kilograms
3. 7 decagrams = How many decigrams?
Solution: 7 decagrams = 7 x 10 grams
= 70 grams
= 70 x 10 decigrams
= 700 decigrams
7 decagrams = 700 decigrams
4. 19 grams 68 milligrams = How many milligrams ?
Solution: 19 gram 68 milligrams = 19 x 10 decigrams + 68 milligrams
= 190 decigrams + 68 milligrams
= (190 x 10) centigrams + 68 milligrams
= 1900 centigrams + 68 milligrams
= 1900 x 10 milligrams + 68 milligrams
= 19000 grams + 68 milligrams
= 19068 milligrams.
19 gram 68 milligrams = 19068 milligrams.
Practice Problems on Metric System Conversions
5. 1000 milligrams = How many kilograms ?
Solution: 1000 milligrams = (1000 ÷ 10) centigrams
= 100 centigrams
= (100 ÷ 10) decigrams
= 10 decigrams
= (10 ÷ 10) gram
= 1 gram
= (1 ÷ 10) decagram
= 01 decagram
= (01 ÷ 10) hectogram
= 0.01 hectogram
= (0.01 ÷ 10) kilogram
= 0.001 kilogram
1000 milligrams = 0.001 kilogram
3.
1. 2 liters = How many kiloliters?
Solution: 2 litres =(2 ÷ 10) decalitre
= 0.2 decalitre
= (0.2 ÷ 10) hectolitre
= 0.02 hectolitre
= (0.02 ÷ 10) kilolitre
= 0.002 kilolitre.
2 litres = 0.002 kilolitre.
2. 23.96 decilitres = How many decalitres?
Solution: 23.96 decilitres = (23.96 ÷ 10) litres
= 2.396 litres
= (2.396 ÷ 10) decalitre
= 0.2396 decalitre
23.96 decilitres = 0.2396 decalitre
3. 63 hectolitres = How many decilitres ?
Solution: 63 hectolitres = (63 x 10) decalitres
= 630 decalitres
= (630 x 10) litres
= 6300 litres
= (6300 x 10) decilitres
= 63000 decilitres.
63 hectolitres = 63000 decilitres.
4. 2123.567 liters = How many milliliters?
Solution: 2123.567 litres = (2123.567 x 10) decilitres
= 21235.67 decilitres
= (21235.67 x 10) centilitres
= 212356.7 centilitres
= (212356.7 x 10) millilitres
= 2123567 millilitres.
2123.567 litres = 2123567 millilitres.
Question 2.
1. 2 cubic kilometers = How many cubic millimeters?
Solution :
2 cubic kilometres = 2×1 km x 1 km x 1 km
= 2 x 10 Hectom. x 10 Hectom. x 10 Hectom.
= 2 x 10 x 10 decam. x 10 x 10 decam. x 10 x 10 decam.
= \(2 \times\left(10^2 \times 10\right) \mathrm{m} \times\left(10^2 \times 10\right) \mathrm{m} \times 10^2 \times 10 \mathrm{~m}\)
= 2 x (\(10^3\) x 10 decim.) x (\(10^3\) x 10 decim.) x (\(10^3\) x 10 decim.)
= 2 x (\(10^4\) x 10 cm) x (\(10^4\) x 10 cm) x (\(10^4\) x 10 cm).
= 2 x (\(10^5\) x 10) mm x (\(10^5\) x 10 mm) x (\(10^5\) x 10 mm)
= 2 x \(10^6\) mm x \(10^6\) mm x \(10^6\) mm
= 2 x \(10^{18}\) cubic millimeters.
2 cubic kilometres = 2 x \(10^{18}\) cubic millimeters.
Alternative process : 2 cubic kilometres = 2 x (1 kilometre)3
= 2 x (10 Hectom.)3
= 2 x (10 x 10 decam.)3
= 2 x (102 x 10 m)3
= 2 x (103 x 10 decim.)3
= 2 x (104 x 10 cm)3
= 2 x (105 x 10 mm)3
= 2 x (106)3 cubicmm
= 2 x 1018 cubicmm
2. 5 x 1016cubic millimeters = How many cubic kilometers?
\(5 \times 10^{16}\) cubic millimetres = \(\left(5 \times 10^{16} \div 10^3\right)\) cubic centimetres
= \(5 \times 10^{13}\) cubic centimeters
= \(\left(5 \times 10^{13} \div 10^3\right)\) cubic decimetres
= \(5 \times 10^{10}\) cubic decimetres
= \(\left(5 \times 10^{10} \div 10^3\right)\) cubic meters
= \(5 \times 10^7\) cubic meters
= \(\left(5 \times 10^7 \div 10^3\right)\) cubic decametres
= \(5 \times 10^4 cubic\) decametres.
= \(\left(5 \times 10^4 \div 10^3\right)\) cubic hectometres
= 5 x 10 cubic hectometres
= \(\left(5 \times 10 \div 10^3\right)\) cubic kilometer
= 5 x 10 / 1000 cubic kilometres
= 5/100 cubic kilometer
= 0.05 cubic kilometers.
\(5 \times 10^{16}\) cubic millimetres = 0.05 cubic kilometers.
Question 3.
1. 1 sq. hectometre = How many square centimeters?
Solution: 1 sq. hectometre = (1 hectometre)
= (1 x 10 decametres)2
= (10 x 10 meters)2
= (100 meters)2
= (100 x 10 decimetres)2
= (1000 decimetres)2
= (1000 x 10 centimetres)2
= (104 centimeters)2
= 108 sq. centimeters.
1 sq. hectometre = 108 sq. centimeters.
Conceptual Questions on Length, Mass, and Volume in Metric Units
2. 6 sq. millimeters = How many sq. decametres?
Solution: 6 sq. millimetres = 6 x (1 mm)2
= 6 x {(1 ÷ 10) cm}2
= 6 x (0.1 cm)2
= 6 x {(0.1 ÷ 10) decimetre}2
= 6 x (0.01 decimetres)2
= 6 x {(0.01 ÷ 10) metre}2
= 6 x (0.001 meters)2
= 6 x {(0.001 ÷ 10) decametre}2
= 6 x (0.0001 decametres)2
= 6 x 0.00000001 sq. decametre
= 0.00000006 sq. decametre
6 sq. millimetres = 0.00000006 sq. decametre
3. 4 x 108 metres = How many ares ?
Solution: 4 x \(10^8\) metres = \(\left(4 \times 10^8 \div 100\right)\) ares
= \(\left(4 \times 10^8 \div 10^2\right)\) ares
= 4 x \(10^6\) ares
4 x \(10^8\) metres = 4 x 10^6 ares
4. 8 x 104ares = How many hectoares ?
Solution: 8 x \(10^4\) ares = \(\left(8 \times 10^4 \div 100\right)\) hectoares
= \(\left(8 \times 10^4 \div 10^2\right. \text { hectoares) }\)
= 8 x \(10^2\) hectoares
= 8 x 100 hectoares
= 800 hectoares.
8 x \(10^4\) ares = 800 hectoares.
5. 56654.92 sq. meters = How many centesimal and how many acres?
Solution: 56654.92 sq. metres = (56654.92 ÷ 40.4678) centesimals
= 1400 centesimals
= (1400 ÷ 100) acres
= 14 acres
56654.92 sq. metres = 14 acres
6. 39.5376 acres = How many hectares?
Solution: 39.5376 acres = (39.5376 ÷ 2.4711) hectoares
= 16 hectares.
39.5376 acres = 16 hectares.
7. 256.6 centesimal = How many bighas ?
Solution: 265.3 centesimals = (265.3 ÷ 1.66) kathas
= 160 kathas
= (160 ÷ 20) bighas
= 8 bighas
265.3 centesimals = 8 bighas
Real-Life Scenarios Involving Measurements in Science
Question 4. How many days and how many years are there in 35040 hours?
Solution: 35040 hours = (35040 ÷24) days
= 1460 days
= (1460 ÷ 365) years
= 4 years.
35040 hours = 4 years.
Examples of Real-Life Applications of the Metric System
Question 5. From the market, you bought pulse 250 gm, atta 500 gm and fish 1 t kg. How many kgs of materials did you buy from the market?
Solution: Total weight = 250 gm + 500 gm + 1 kg
= 250/1000 kg + 500/1000 kg + 1kg
= 0.25 kg + 0.5 kg + 1 kg
= 1.75 kg
∴ You bought 1.75 kg of materials from the market.
Question 6. The distance between your school from your house is 2.04 kilometers. If you would be cycling at a speed of 10.2 kilometers per hour, how long should you take to reach the school?
Solution: We know, time = Distance/Speed
Here, distance = 2.04 km, speed = 10.2 km / hour
∴ Time = 2.04/10.2 hour
= 204/1020 hour
= 0.2 hour
= 0.2 x 60 minutes
= 12.0 minutes.
∴ The required time = is 12 minutes.
Question 7. Diana has 14.4 meters of cloth in her house. If 1.8 meters of cloth is required to make each frock, how many frocks can be made by Diana?
Solution: Total cloth = 14.4 meters.
Cloth required for 1 frock =1.8 meters.
∴ The required number of frocks = 14.4 / 1.8
= 144/18
= 8.
So Diana can make 8 frocks with the cloth that she has in her house.
From a bamboo of length 15.77 meters, 2.25 meters is cut off. The remaining part is divided into 4, equal parts. What is the length of each part?
Solution: Total length of the bamboo = 15.77 meters.
Cut-off a length of the bamboo = 2.25 meters.
∴ The length of the remaining part of the bamboo = (15.77 – 2.25) meters
= 13.52 meters
It is subdivided into 4 equal parts.
The length of each part = (13.52 ÷ 4) meters
= 3.38 meters.
The length of each part is 3.38 meters.