CONVERTING SCIENTIFIC NOTATION TO NUMBERS EXAMPLES

Solved Examples

Example 1 :

Write the following numbers in decimal form:

(i) 3.459 x 10⁶

Solution :

3.459 x 10⁶

Since we have positive sign for the power of 10, we have to the move the decimal point 6 digit to the right side.

  =  3459000

(ii) 5.678 10⁴ 

Solution :

Since we have positive sign for the power of 4, we have to the move the decimal point 4 digit to the right side.

  =  56780

(iii) 1.00005 x 10^-5 

Solution :

Since we have negative sign for the power of 5, we have to the move the decimal point 5 digit to the left side.

  =  0.0000100005

(iv) 2.530009 x 10^-7

Solution :

Since we have negative sign for the power of 7, we have to the move the decimal point 7 digits to the left side.

  =  0.0000002530009

Arithmetic with Numbers in Scientific Notation

Example 2 :

Represent the following numbers in scientific notation:

(i)  (300000)² x (20000)⁴

Solution :

  =  (300000)² x (20000)⁴

  =  (3.0 x 10⁵)² x (2.0 x 10⁴)⁴

  =  3² x 10¹⁰ x 2⁴ x 10¹⁶

  =  144 x 10¹⁰⁺¹⁶

  =  1.44 x 10² x  10¹⁰⁺¹⁶

  =  1.44 x 10²⁸

(ii)  (0.000001)¹¹ ÷ (0.005)³

Solution :

  =  (0.000001)¹¹ ÷ (0.005)³

  =  (1 x 10^-6)¹¹ ÷ (5 x 10^-3)³

  =  (1/125) x 10^-66 x 10⁹

  =  0.008 x 10^-66+9

  =  8 x 10^-3 x 10^-57

  =  8 x 10^-57-3

  =  8 x 10^-60

(iii)  {(0.00003)⁶ x (0.00005)⁴} ÷ {(0.009)³ x (0.05)²}

Solution :

  =  {(0.00003)⁶ x (0.00005)⁴} ÷ {(0.009)³ x (0.05)²}

  =  {(3x10^-5)⁶ x (5x10^{- 5})⁴} ÷ {(9x10^-3)³ x (5x10^-2)²}

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