1. Write the following numbers in the expanded forms:
(a) 279404
Solution:-
The expanded form of the number 279404 is,
= (2 × 100000) + (7 × 10000) + (9 × 1000) + (4 × 100) + (0 × 10) + (4 × 1)
Now we can express it using powers of 10 in the exponent form,
= (2 × 105) + (7 × 104) + (9 × 103) + (4 × 102) + (0 × 101) + (4 × 100)
(b) 3006194
Solution:-
The expanded form of the number 3006194 is,
= (3 × 1000000) + (0 × 100000) + (0 × 10000) + (6 × 1000) + (1 × 100) + (9 × 10) + (4 × 1)
Now we can express it using powers of 10 in the exponent form,
= (3 × 106) + (0 × 105) + (0 × 104) + (6 × 103) + (1 × 102) + (9 × 101) + (4 × 100)
(c) 2806196
Solution:-
The expanded form of the number 2806196 is,
= (2 × 1000000) + (8 × 100000) + (0 × 10000) + (6 × 1000) + (1 × 100) + (9 × 10) + (6 × 1)
Now we can express it using powers of 10 in the exponent form,
= (2 × 106) + (8 × 105) + (0 × 104) + (6 × 103) + (1 × 102) + (9 × 101) + (6 × 100)
(d) 120719
Solution:-
The expanded form of the number 120719 is,
= (1 × 100000) + (2 × 10000) + (0 × 1000) + (7 × 100) + (1 × 10) + (9 × 1)
Now we can express it using powers of 10 in the exponent form,
= (1 × 105) + (2 × 104) + (0 × 103) + (7 × 102) + (1 × 101) + (9 × 100)
(e) 20068
Solution:-
The expanded form of the number 20068 is,
= (2 × 10000) + (0 × 1000) + (0 × 100) + (6 × 10) + (8 × 1)
Now we can express it using powers of 10 in the exponent form,
= (2 × 104) + (0 × 103) + (0 × 102) + (6 × 101) + (8 × 100)
2. Find the number from each of the following expanded forms:
(a) (8 × 10)4 + (6 × 10)3 + (0 × 10)2 + (4 × 10)1 + (5 × 10)0
Solution:-
The expanded form is,
= (8 × 10000) + (6 × 1000) + (0 × 100) + (4 × 10) + (5 × 1)
= 80000 + 6000 + 0 + 40 + 5
= 86045
(b) (4 × 10)5 + (5 × 10)3 + (3 × 10)2 + (2 × 10)0
Solution:-
The expanded form is,
= (4 × 100000) + (0 × 10000) + (5 × 1000) + (3 × 100) + (0 × 10) + (2 × 1)
= 400000 + 0 + 5000 + 300 + 0 + 2
= 405302
(c) (3 × 10)4 + (7 × 10)2 + (5 × 10)0
Solution:-
The expanded form is,
= (3 × 10000) + (0 × 1000) + (7 × 100) + (0 × 10) + (5 × 1)
= 30000 + 0 + 700 + 0 + 5
= 30705
(d) (9 × 10)5 + (2 × 10)2 + (3 × 10)1
Solution:-
The expanded form is,
= (9 × 100000) + (0 × 10000) + (0 × 1000) + (2 × 100) + (3 × 10) + (0 × 1)
= 900000 + 0 + 0 + 200 + 30 + 0
= 900230
3. Express the following numbers in standard form:
(i) 5,00,00,000
Solution:-
The standard form of the given number is 5 × 107
(ii) 70,00,000
Solution:-
The standard form of the given number is 7 × 106
(iii) 3,18,65,00,000
Solution:-
The standard form of the given number is 3.1865 × 109
(iv) 3,90,878
Solution:-
The standard form of the given number is 3.90878 × 105
(v) 39087.8
Solution:-
The standard form of the given number is 3.90878 × 104
(vi) 3908.78
Solution:-
The standard form of the given number is 3.90878 × 103
4. Express the number appearing in the following statements in standard form.
(a) The distance between Earth and Moon is 384,000,000 m.
Solution:-
The standard form of the number appearing in the given statement is 3.84 × 108m.
(b) Speed of light in a vacuum is 300,000,000 m/s.
Solution:-
The standard form of the number appearing in the given statement is 3 × 108m/s.
(c) Diameter of the Earth is 1,27,56,000 m.
Solution:-
The standard form of the number appearing in the given statement is 1.2756 × 107m.
(d) Diameter of the Sun is 1,400,000,000 m.
Solution:-
The standard form of the number appearing in the given statement is 1.4 × 109m.
(e) In a galaxy, there are, on average, 100,000,000,000 stars.
Solution:-
The standard form of the number appearing in the given statement is 1 × 1011 stars.
(f) The universe is estimated to be about 12,000,000,000 years old.
Solution:-
The standard form of the number appearing in the given statement is 1.2 × 1010 years old.
(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.
Solution:-
The standard form of the number appearing in the given statement is 3 × 1020m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
Solution:-
The standard form of the number appearing in the given statement is 6.023 × 1022 molecules.
(i) The Earth has 1,353,000,000 cubic km of seawater.
Solution:-
The standard form of the number appearing in the given statement is 1.353 × 109 cubic km.
(j) The population of India was about 1,027,000,000 in March 2001.
Solution:-
The standard form of the number appearing in the given statement is 1.027 × 109.
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