Exponents (Exercise 6.3) RD Sharma Solutions | Mathematics (Maths) Class 7 PDF Download

 Page 1


 
 
 
 
 
 
 
Exercise 6.3         Page No: 6.30 
 
Express the following numbers in the standard form: 
(i) 3908.78 
(ii) 5,00,00,000 
(iii) 3,18,65,00,000 
(iv) 846 × 10
7
 
(v)723 × 10
9 
 
Solution: 
(i) Given 3908.78 
3908.78 = 3.90878 x 10
3
 [since the decimal point is moved 3 places to the left] 
 
(ii) Given 5,00,00,000 
5,00,00,000 = 5,00,00,000.00 = 5 x 10
7
 [since the decimal point is moved 7 places to the 
left] 
 
(iii) Given 3,18,65,00,000  
3,18,65,00,000 = 3,18,65,00,000.00 
= 3.1865 x 10
9
 [since the decimal point is moved 9 places to the left] 
 
(iv) Given846 × 10
7
 
846 × 10
7
 = 8.46 x 10
2
 x 10 [since the decimal point is moved 2 places to the left] 
= 8.46 x 10
9
 [since a
m
 x a
n
 = a
m+n
] 
 
(v) Given 723 × 10
9
    
723 × 10
9
 = 7.23 x 10
2
 x 10
9
 [since the decimal point is moved 2 places to the left] 
= 7.23 x 10
11
 [ since a
m
 x a
n
 = a
m+n
]  
 
2. Write the following numbers in the usual form:  
(i) 4.83 × 10
7
 
(ii) 3.21 × 10
5
 
(iii) 3.5 × 10
3
 
 
Solution: 
(i) Given 4.83 × 10
7
  
4.83 × 10
7
 = 483 × 10
7-2
 [since the decimal point is moved two places to the right] 
Page 2


 
 
 
 
 
 
 
Exercise 6.3         Page No: 6.30 
 
Express the following numbers in the standard form: 
(i) 3908.78 
(ii) 5,00,00,000 
(iii) 3,18,65,00,000 
(iv) 846 × 10
7
 
(v)723 × 10
9 
 
Solution: 
(i) Given 3908.78 
3908.78 = 3.90878 x 10
3
 [since the decimal point is moved 3 places to the left] 
 
(ii) Given 5,00,00,000 
5,00,00,000 = 5,00,00,000.00 = 5 x 10
7
 [since the decimal point is moved 7 places to the 
left] 
 
(iii) Given 3,18,65,00,000  
3,18,65,00,000 = 3,18,65,00,000.00 
= 3.1865 x 10
9
 [since the decimal point is moved 9 places to the left] 
 
(iv) Given846 × 10
7
 
846 × 10
7
 = 8.46 x 10
2
 x 10 [since the decimal point is moved 2 places to the left] 
= 8.46 x 10
9
 [since a
m
 x a
n
 = a
m+n
] 
 
(v) Given 723 × 10
9
    
723 × 10
9
 = 7.23 x 10
2
 x 10
9
 [since the decimal point is moved 2 places to the left] 
= 7.23 x 10
11
 [ since a
m
 x a
n
 = a
m+n
]  
 
2. Write the following numbers in the usual form:  
(i) 4.83 × 10
7
 
(ii) 3.21 × 10
5
 
(iii) 3.5 × 10
3
 
 
Solution: 
(i) Given 4.83 × 10
7
  
4.83 × 10
7
 = 483 × 10
7-2
 [since the decimal point is moved two places to the right] 
 
 
 
 
 
 
 
= 483 × 10
5
  
= 4, 83, 00,000 
 
(ii) Given 3.21 × 10
5  
3.21 × 10
5 
= 321 x 10
5-2
 [since the decimal point is moved two places to the right] 
= 321 x 10
3
  
= 3, 21,000 
 
(iii) Given 3.5 × 10
3
  
3.5 × 10
3
 = 35 x 10
3-1
 [since the decimal point is moved one place to the right] 
= 35 x 10
2
  
= 3,500 
 
3. Express the numbers appearing in the following statements in the standard form: 
(i) The distance between the Earth and the Moon is 384,000,000 meters. 
(ii) Diameter of the Earth is 1, 27, 56,000 meters. 
(iii) Diameter of the Sun is 1,400,000,000 meters. 
(iv) The universe is estimated to be about 12,000,000,000 years old. 
 
Solution: 
(i) Given the distance between the Earth and the Moon is 384,000,000 meters. 
The distance between the Earth and the Moon is 3.84 x 10
8
 meters. 
[Since the decimal point is moved 8 places to the left.] 
 
(ii) Given diameter of the Earth is 1, 27, 56,000 meters. 
The diameter of the Earth is 1.2756 x 10
7
 meters. 
[Since the decimal point is moved 7 places to the left.] 
 
(iii) Given diameter of the Sun is 1,400,000,000 meters. 
The diameter of the Sun is 1.4 x 10
9
 meters. 
[Since the decimal point is moved 9 places to the left.] 
 
(iv) Given the universe is estimated to be about 12,000,000,000 years old. 
The universe is estimated to be about 1.2x 10
10
 years old. 
[Since the decimal point is moved 10 places to the left.]