The document RD Sharma Solutions - Ex-6.3, Exponents, Class 7, Math Class 7 Notes | EduRev is a part of the Class 7 Course RD Sharma Solutions for Class 7 Mathematics.

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**Q1 Express the following numbers in the standard form**

**(i) 3908.78**

**(ii) 5,00,00,000**

**(iii) 3,18,65,00,000**

(iv) 846Ã—10^{7}

(v) 723Ã—10^{9}

**Sol:**

(i) 3908.78 = 3.90878Ã—10^{3}

Since, the decimal point is moved three places to the left

(ii) 5,00,00,000 = 5,00,00,000.00

= 5Ã—10^{7}

Since, the decimal point is moved seven places to the left

(iii) 3,18,65,00,000 = 3,18,65,00,000.00

= 3.1865Ã—10^{9}

Since, the decimal point is moved nine places to the left

(iv) 846Ã—10^{7} = 8.46Ã—10^{2}Ã—10^{7}

= 8.46Ã—10^{9}

Since, the decimal point is moved two places to the left

(v) 723Ã—10^{9} = 7.23Ã—10^{2}Ã—10^{9}

= 7.23Ã—10^{11}

Since, the decimal point is moved two places to the left

**Q2. Write the following numbers in the usual form**

(i) 4.83Ã—10^{7}

(ii) 3.21Ã—10^{5}

(iii) 3.5Ã—10^{3}

**Sol:**

(i) 4.83Ã—10^{7} = 483Ã—10^{(7âˆ’2)}

= 483Ã—10^{5}

= 4,83,00,000

Since, the decimal point is moved two places to the right

(ii) 3.21Ã—10^{5} = 321Ã—10^{(5âˆ’2)}

= 321Ã—10^{3}

= 3,21,000

Since, the decimal point is moved two places to the right

(ii) 3.5Ã—10^{3} = 35Ã—10^{(3âˆ’1)}

= 35Ã—10^{2}

= 3,500

Since, the decimal point is moved one place to the right

**Q3. 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 metres.**

**(ii) Diameter of the earth is 1,27,56,000 metres.**

**(iii) Diameter of the sun is 1,400,000,000 metres.**

**(iv) The universe is estimated to be about 12,000,000,000 years old.**

**Sol:**

(i) The distance between the earth and the moon is 3.84Ã—10^{8} metres.

Since, the decimal point is moved eight places to the left

(ii) Diameter of the earth is 1.2756Ã—10^{7} metres.

Since, the decimal point is moved seven places to the left

(ii) Diameter of the sun is 1.4Ã—10^{9} metres.

Since, the decimal point is moved nine places to the left

(iv) The universe is estimated to be about 1.2Ã—10^{10} years old.

Since, the decimal point is moved ten places to the left