Scientific notation/Standard form:

               In scientific notation, a number is expressed as some power of ten multiplied by a number between 1 and 10.

 Examples:

3. The Moon is 384000000 meters away from the Earth. The distance of the moon from the Earth can also be expressed as 3.84 x 10⁸ This saves writing down or interpreting large numbers of zeros.
4. A number 62750 can be expressed as 6.275 x 10⁴. Similarly, the standard form of 0.00045 is 4.5 x 10^-4

   Quick Quiz

1. Name five prefixes most commonly used.

Ans:     (1) kilo (k) = 10³      (2) centi(c)10^-2        (3) milli(m) = 10^-3

            (4) micro (u) = 10^-6        (5) mega (M) = 10⁶

 

2.The Sun is one hundred and fifty million kilometres away from the Earth. Write this.

(a) as an ordinary whole number

(b) In scientific notation.

 

Ans:    The distance of Sun from the Earth = 150 million km         

(A) as an ordinary whole number:

           = 150 x 10⁶km= 150 x 10⁶ x 10³m                                         1 million 10⁶ 1 kilo = 10³

                = 150000000000 m

(B) In scientific notation.

= 150 x 10⁶ x 10³

= 150 x 10⁹

 = 15 x 10 x 10⁹

= 15 x 10¹⁰

 

= 15 ÷ 10 x 10 x 10¹⁰

=1.5 x 10¹¹

=1.5 x 10¹¹ m

 

3. Write the numbers given below in scientific notation.

1. 3000000000 ms^-1 C.6400000 m
2. 0000000016 g       D. 0.0000548 s

Ans:

A. 3000000000 ms-1

= 3 x 1000000000 ms^-1

= 3x 10⁹ ms^-1 

 

B. 6400000 m

= 64 x 10⁵m

= 6.4 x 10 x 10⁵

= 6.4 x 10⁶m

 

C. 0000000016 g

= 0.0000000016 ÷ 10000000000 g

= 16 x 10^-10g

            =1.6x 10x 10^-10g

           =1.6x10^-9g

 

D. 0.0000548 s

 = 0.0000548

=    0.0000548 ÷10000000

=    548 x 10^-7

= 5.48 x 10² x 10^-7

=5.48x 10^-5 s 

 

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