**What do you understand by scientific notation?**

Difficulty: Hard

**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:**

^{8}This saves writing down or interpreting large numbers of zeros.^{4}. 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) = 10^{3 } **(2) **centi(c)10^{-2} ** (3)** milli(m) = 10^{-3}

** (4)** micro (u) = 10^{-6} ** (5)** mega (M) = 10^{6}

^{ }

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

**(a) **as an ordinary whole number

**(b) I**n scientific notation.

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

**(A) as an ordinary whole number:**

= 150 x 10^{6}km= 150 x 10^{6} x 10^{3}m 1 million 10^{6} 1 kilo = 10^{3}

^{ }= 150000000000 m

**(B) In scientific notation.**

= 150 x 10^{6} x 10^{3}

= 150 x 10^{9}

= 15 x 10 x 10^{9}

= 15 x 10^{10}

= 15 ÷ 10 x 10 x 10^{10}

=1.5 x 10^{11}

=1.5 x 10^{11} m

**3. Write the numbers given below in scientific notation.**

- 3000000000 ms
^{-1}**C**.6400000 m - 0000000016 g
**D.**0.0000548 s

**Ans:**

**A. 3000000000 ms-1**

= 3 x 1000000000 ms^{-1}

= 3x 10^{9} ms^{-1}

**B. 6400000 m**

= 64 x 10^{5}m

= 6.4 x 10 x 10^{5}

= 6.4 x 10^{6}m

**C. 0000000016 g**

= 0.0000000016 ÷ 10000000000 g

= 16 x 10^{-10}g

=1.6x 10x 10^{-10}g

=1.6x10^{-9}g

**D. 0.0000548 s**

= 0.0000548

= 0.0000548 ÷10000000

= 548 x 10^{-7}

= 5.48 x 10^{2} x 10^{-7}

=5.48x 10^{-5 }s

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