**Converting Scientific Notation to Numbers Examples :**

Here we are going to see some example problems of converting scientific notation to numbers.

Th e reverse process of converting a number in scientifi c notation to the decimal form is easily done when the following steps are followed:

(i) Write the decimal number.

(ii) Move the decimal point by the number of places specified by the power of 10, to the right if positive, or to the left if negative. Add zeros if necessary.

(iii) Rewrite the number in decimal form.

**Example 1 :**

Write the following numbers in decimal form:

(i) 3.459 x 10^{6}

**Solution :**

3.459 x 10^{6}

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 10^{4}

**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

**Example 2 :**

Represent the following numbers in scientific notation:

(i) (300000)^{2} x (20000)^{4}

**Solution :**

= (300000)^{2} x (20000)^{4}

= (3.0 x 10^{5})^{2 }x (2.0 x 10^{4})^{4}

= 3^{2} x 10^{10}^{ }x 2^{4} x 10^{16}

= 144 x 10^{10+16}

= 1.44 x 10^{2} x 10^{10+16}

= 1.44 x 10^{28}

(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 10^{9}

= 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}}

After having gone through the stuff given above, we hope that the students would have understood how to convert a number from scientific notation to standard form.

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