EX.13.3 Q4 Exponents-and-Powers Solutions- NCERT Maths class 7

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Question

Express the number appearing in the following statements in standard form.

(a) The distance between Earth and Moon is \(384,000,000 \rm\, m\)

(b) Speed of light in vacuum is \(300,000,000 \rm \,m/s\)

(c) Diameter of the Earth is \(1,27,56,000\rm \,m\)

(d) Diameter of the Sun is \(1,400,000,000 \rm\,m\)

(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 \(300,000,000,000,000,000,000 \rm\,m\)

(h) \(60,230,000,000,000,000,000,000\) molecules are contained in a drop of water weighing \(1.8 \rm\,gm\)

(i) The earth has \(1,353,000,000\) cubic \(\rm{km}\) of sea water

(j) The population of India was about \(1,027,000,000\) in March \(2001\)

Text Solution

(a) The distance between Earth and Moon is \(384,000,000 \rm\, m\).

Standard Form \(= 3.84\times10^{8} \rm\, m\)

(b) Speed of light in vacuum is \(300,000,000 \rm \,m/s\).

Standard Form \(= 3\times10^{8} \rm \, m/s\)

(c) Diameter of the Earth is \(1,27,56,000\rm \,m\).

Standard Form \(= 1.2756\times10^{7}\rm\, m\)

(d) Diameter of the Sun is \(1,400,000,000 \rm\,m\).

Standard Form \(= 1.4\times10^{9} \rm\,m\)

(e) In a galaxy there are on an average \(100,000,000,000\) stars.

Standard Form \(= 1\times10^{11}\) stars

(f) The universe is estimated to be about \(12,000,000,000\) years old.

Standard Form \(= 1.2\times10^{10} \)years old

(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be \(300,000,000,000,000,000,000 \rm\,m\).

Standard Form \(= 3\times10^{20}\rm\, m\)

(h)  \(60,230,000,000,000,000,000,000\) molecules are contained in a drop of water weighing \(1.8 \rm\,gm\).

Standard Form \(= 6.023\times10^{22}\) molecules

(i) The earth has \(1,353,000,000\) cubic \(\rm{km}\) of sea water.

Standard Form \(= 1.353\times10^{9} \rm cubic \,\rm\, km\)

(j) The population of India was about \(1,027,000,000\) in March \(2001\).

Standard Form \(= 1.027\times10^{9}\)

  
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