# Scientific Notations

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 × 108 m/sec

#### Note:

•  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.

## Numbers with decimal point

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.

#### Note:

•  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× 103

25,950
=2.595 × 10,000
= 2.595 × 104

## 1. 3,230,000

#### Explanation:

3,230,000
= 3.23 × 1,000,000
= 3.23 × 106

## 2. 10,020,000,000

#### Explanation:

10,020,000,000
=1.002 × 10,000,000,000
= 1.002 × 1010

## 1. Area of the earth's surface is approximately 51 00,00,000 sq m

#### Explanation:

51 00,00,000 sq m
= 51× 1,00,00,000
= 51× 107
= 5.1× 10×107
= 5.1× 108 sq km

## 2. Diameter of a hydrogen molecule is 0.0000000000027 m. Write it as Scientific notation.

#### Explanation:

0. 0000000000027 m
= 27/100000000000
= 27/ 1011
= 27× 10-11
=2.7× 10-10 m

## The total extent of land in a village is about 3.75 × 104 acres. How to express the number in standard form?

#### Explanation:

Land in a village is about 3.75 × 10 4 acres
= 3.75 × 10 4
= 3.75 ×10×10×10×10
= 3.75 ×10000
= 37500

## The weight of 100 books

#### Explanation:

= 0.3 × 102 ×100
= 0.3 × 104
= 0.3 × 10× 10 × 10× 10
= 3000 kg.

## How to multiply Scientific notation

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

Let us say,
(x×10a) × (y×10b)
Multiply the numbers (x×y)
So that, (x×10a) × (y×10b) = (x×y) × 10a+b

## 1. (5×10a) × (2×10b)

#### Explanation:

(5×10a) × (2×10b)
Multiply the numbers and add the exponent of 10.
= (5×2) × 10a+b
= (10) × 10a+b

## 1. (8×105) × (7×102)

#### Explanation:

(8×105) × (7×102)
Multiply the numbers and add the exponent of 10.
= (8×7) × 105+2
=(56) × 107
=5,60,00,0000
= 5.6× 108

## How to divide Scientific notation

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

Let us say,
(x×10a) ÷ (y×10b)
Divide the numbers (x/y)
Subtract the exponents of 10. 10a-b
So that, (x×10a) ÷ (y×10b) = (x/y) × 10a-b

## 1. (10×10a) ÷ (5×10b)

#### Explanation:

(10×10a) ÷ (5×10b)
Divide the numbers and subtract the exponents of 10.
= (10/5) × 10a-b
= 2× 10a-b

## 1. (75×108) ÷ (5×104)

#### Explanation:

(75×108) ÷ (5×104)
= (75/5) × 108-4
= 15× 104

## 1. (8×105) × (7×102) / (4×105)

#### Explanation:

(8×105) × (7×102) / (4×105)
= (8×7) × 105+2/ (4×105)
= (56× 107) ÷ 4×105
= 56/4 × 107-5
= 14× 102
= 1400
= 1.4× 103

## Distance between the sun and the earth is 15,00,00,000 km. Speed of light is 300,000,000 m/s. How long it takes to reach the light to the earth?

#### Explanation :

Speed of light is 300,000,000 m/s. = 300,000 km/s= 3× 105
Distance between the sun and the earth is 15,00,00,000 km.= 15,00,00,000 km= 15 × 107
We have to find the time that sun's light to reach to the earth.
Now time= distance / speed
So that, if we put the values here for distance and speed we can find the time
Time= distance / speed
= 15× 107/ 3× 105
= 5× 107-5
= 5× 102

## Worksheets

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