write the following in decimal form:
5+10²+4×10⁰+9×10^-2+6×10^-3
Answers
The given numbers are 279404, 3006194, 2806196, 120719 and 20068.
The expansion of number is,
The expansion of number is,
The expansion of number is,
The expansion of number is,
The expansion of number is,
Question 2
Find the number from each of the following expanded forms: (a) 8 ×10⁴ + 6 ×10³ + 0×10² + 4×10¹ + 5×10⁰ (b) 4 ×10⁵ + 5×10³ + 3×10² + 2×10⁰ (c) 3 ×10⁴ + 7×10² + 5×10⁰ (d) 9 ×10⁵ + 2×10² + 3×10¹
Answer:
(a)
Simplify the given expanded form of number.
Thus, the number is .
(b)
Simplify the given expanded form of number.
Thus, the number is .
(c)
Simplify the given expanded form of number.
Thus, the number is .
(d)
Simplify the given expanded form of number.
Thus, the number is .
Question 3
Express the following numbers in standard form: (i) 5,00,00,000 (ii) 70,00,000 (iii) 3,18,65,00,000 (iv) 3,90,878 (v) 39087.8 (vi) 3908.78
Answer:
The standard form of number can be expressed as a decimal number between and multiplied by the power of .
Where is the decimal number and is power of .
(i)
The given number is .
The standard form representation of is,
Thus, the standard form is .
(ii)
The given number is .
The standard form representation of is,
Thus, the standard form is .
(iii)
The given number is .
The standard form representation of is,
Thus, the standard form is .
(iv)
The given number is .
The standard form representation of is,
Thus, the standard form is .
(v)
The given number is .
The standard form representation of is,
Thus, the standard form is .
(vi)
The given number is .
The standard form representation of is,
Thus, the standard form is .
Question 4
Express the number appearing in the following statements in standard form. (a) The distance between Earth and Moon is 384,000,000 m. (b) Speed of light in vacuum is 300,000,000 m/s. (c) Diameter of the Earth is 1,27,56,000 m. (d) Diameter of the Sun is 1,400,000,000 m. (e) In a galaxy there are on an average 100,000,000,000 stars. (f) The universe is estimated to be about 12,000,000,000 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. (h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm. (i) The earth has 1,353,000,000 cubic km of sea water. (j) The population of India was about 1,027,000,000 in March, 2001.
Answer:
The standard form of number can be expressed as a decimal number between and multiplied by the power of .
Where is the decimal number and is power of .
(a)
Given that the distance between Earth and Moon is .
The standard form of is,
(b)
Given that the speed of light in vacuum is .
The standard form of is,
(c)
Given that the diameter of the earth is .
The standard form of is,
(d)
Given that the diameter of the sun is .
The standard form of is,
(e)
Given that the number of stars in galaxy is .
The standard form of is,
(f)
Given that universe is old.
The standard form of is,
(g)
Given that the distance of the Sun from centre of Milky Way is .
The standard form of is,
(h)
Given that the number of molecule in drop of water is .
The standard form of is,
(i)
Given that the earth has of sea water.
The standard form of is,
(j)
Given that the population of India in march, 2001 is .
The standard form of is,
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