We can write very big or small numbers or remember them easily with the help of scientific notation of numbers.

Let us say,
the speed of light in the air is approximately **30,00,00,000 m/sec.**

To write this number as **powers of 10,**

First write it as product of two numbers.

30, 00, 00, 000 =3 × 10,00,00,000

Count the number of zeros to write index of 10. 3 × 10^{8} m/sec

- Scientific notation of numbers is written as powers of 10.
- From which first number is between 1 to 10 and the second is written as power of 10.

In order to write the given numbers with decimal point as a power of 10, Move the decimal point over to the right until the coefficient lies between 1 to 10.

- For each place shift the decimal in excess of the exponent will be lowered 1 power of 10.

**2654.4**

= 2.6544 × 1000

= 2.6544× 10^{3}

**25,950**

=2.595 × 10,000

= 2.595 × 10^{4}

**3,230,000**

= 3.23 × 1,000,000

**= 3.23 × 10 ^{6} **

**10,020,000,000**

=1.002 × 10,000,000,000

= 1.002 × 10^{10}

**51 00,00,000 sq m**

= 51× 1,00,00,000

= 51× 10^{7}

= 5.1× 10×10^{7}

= **5.1× 10 ^{8} **sq km

0. 0000000000027 m

= `27/100000000000`

= 27/ 10^{11}

= 27× 10^{-11}

**=2.7× 10**^{-}^{10 }m

= `27/100000000000`

= 27/ 10

= 27× 10

**Land in a village is about 3.75 × 10 ^{4} acres**

= 3.75 × 10

= 3.75 ×10×10×10×10

= 3.75 ×10000

= 37500

**= 0.3 × 10 ^{2} ×100**

= 0.3 × 10

= 0.3 × 10× 10 × 10× 10

= 3000 kg.

To multiply numbers given in Scientific notation multiply the numbers and add the exponents of 10.

Multiply the numbers (x×y)

Add the exponents of 10.

So that, (x×10

**(5×10 ^{a}) × (2×10^{b})**

Multiply the numbers and add the exponent of 10.

= (5×2) × 10

**(8×10 ^{5}) × (7×10^{2}) **

= (8×7) × 10

=(56) × 10

=5,60,00,0000

To divide numbers given in Scientific notation divide the numbers and subtract the exponents of 10.

Divide the numbers (x/y)

Subtract the exponents of 10. 10

So that, (x×10

**(10×10 ^{a}) ÷ (5×10^{b})**

= `(10/5)` × 10

**(75×10 ^{8}) ÷ (5×10^{4})**

= `(75/5)` × 10

= 15× 10

**(8×10 ^{5}) × (7×10^{2}) / (4×10^{5})**

= (8×7) × 10

= (56× 10

= 56/4 × 10

= 14× 10

= 1400

**Speed of light is 300,000,000 m/s. = 300,000 km/s= 3× 10^{5}**

Distance between the sun and the earth is 15,00,00,000 km.= 15,00,00,000 km= 15

We have to find the time that sun's light to reach to the earth.

So that, if we put the values here for distance and speed we can find the time

Time= distance / speed

= 15× 10

= 5× 10

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