Class 8 Maths Ch12 Exponent and Powers Ex12.2-NCERT
Ex 12.2 Class 8 Maths Question 1.
Express the following numbers in standard form:
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000
Solution:
(v) 31860000000
= 3.186 × 10000000000
= 3.186 × 1010
Hence, the required standard from = 3.186 × 1010
Ex 12.2 Class 8 Maths Question 2.
Express the following numbers in usual form.
(i) 3.02 × 10-6
(ii) 4.5 × 104
(iii) 3 × 10-8
(iv) 1.0001 × 109
(v) 5.8 × 1012
(vi) 3.61492 × 106
Solution:
Ex 12.2 Class 8 Maths Question 3.
Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to \frac { 1 }{ 1000000 } m.
(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb
(iii) Size of a bacteria is 0.0000005 m
(iv) Size of a plant cell is 0.00001275 m
(v) Thickness of a thick paper is 0.07 mm.
Solution:
Ex 12.2 Class 8 Maths Question 4.
In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?
Solution:
Thickness of books = 5 × 20 = 100 mm
Thickness of 5 paper sheets = 5 × 0.016 mm = 0.080 mm.
Total thickness of the stack = 100 mm + 0.080 mm = 100.080 mm = 1.0008 × 102 mm
Ex 13.1 Class 8 Maths Question 1.
Following are the car parking charges near a railway station up to.
4 hours – ₹ 60
8 hours – ₹ 100
12 hours – ₹ 140
24 hours – ₹ 180
Check if the parking charges are in direct proportions to the parking time.
Solution:
We have the ratio of time period and the parking charge.
Hence the given quantities are not directly proportional.
Ex 13.1 Class 8 Maths Question 2.
A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.
Solution:
Let the number to be filled in the blanks be a, b, c and d respectively.
Ex 13.1 Class 8 Maths Question 3.
In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base?
Solution:
Let the required red pigment be x part.
Hence, the required amount of red pigment = 24 parts.
Ex 13.1 Class 8 Maths Question 4.
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Solution:
Let the required number of bottles be x.
Hence the required number of bottles = 700.
Ex 13.1 Class 8 Maths Question 5.
A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?
Solution:
Let the actual length be x cm.
Ex 13.1 Class 8 Maths Question 6.
In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship?
Solution:
Let the required length of the model ship be x m.
Ex 13.1 Class 8 Maths Question 7.
Suppose 2 kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in
(i) 5 kg of sugar?
(ii) 1.2 kg of sugar?
Solution:
Let x be the number of sugar crystals needed.
Ex 13.1 Class 8 Maths Question 8.
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road of 72 km. What would be her distance covered in the map?
Solution:
Let the required distance be x km.
Hence the distance covered in the map = 4 cm.
Ex 13.1 Class 8 Maths Question 9.
A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time
(i) the length of the shadow cast by another pole 10 m 50 cm high,
(ii) the height of a pole which casts a shadow 5 m long.
Solution:
(i) Let the required length of shadow be x m.
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