Numbers are the essential part of our life. We study about different types of number and various operations of them. In mathematics, we also come across the numbers as small as negligible and as big as infinity. Both types of number may have a very lengthy notation. For instance - 0.00000000000001 is a very small number. On the other hand, a very big number may be 9809534740945790435900749450943540. It is quite inconvenient to write and work with the numbers like this.

For the ease of writing and calculation, the scientific notation of writing such numbers was introduced. Scientific notation is also known as **standard notation** or **standard form** or sometimes **exponential notation**. It is all about the way we write the numbers that has too big or a too small value. It is a special way of writing the numbers, to make it easier to use. It also helps us write a big or small value in a convenient way of standard decimal notation. In the scientific notation, a number is written in the following way -

$x \times 10^{y}$

According to a simple example -

100000 can be written in scientific notation as 1 x 10$^{5}$.

Let us go ahead and learn more about scientific notation.

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Scientific notation is a shorter method to express very large numbers. This is used to express very large or very small numbers. This method is known as scientific notation.

Scientific Notation is expressed as the powers of the base number 10. Under scientific notation, a number is written as the product of a number (integer or decimal) and a power of 10. Scientific notation is also known as standard form or as exponential notation.

Scientific notation for kids:

We know the speed of light 300,000,000 m/sec.

We know the speed of light 300,000,000 m/sec.

This is a very large number for written.

For this issue, we are used scientific notation to express very large to a simple number.

300,000,000 m/sec = 3 X 10^{8}

Use the below widget to convert the number into scientific notation.

Scientific notation is defined as shorter method to express very large numbers this is called scientific notation. Scientific Notation is based on powers of the base number 10 has expressed in the scientific notation.

**For example:**

This notation also called as short form.

The scientific notation of 2340000000 this can be written as 2.34 x 10^{ 9}

And the another method is 0.000021 = 2.1 x 10 ^{-5}

The numbers that has too big or a too small value can be expressed in the form a x 10^{n}, where 1 $\leq$ a < 10 and n > 0 for very large numbers and n < 0 for very small numbers.

The constants *a* and *n* are respectively called as the base and exponent of the scientific notation.

Thus, the velocity of light is expressed as 6.71 x 10^{8 }miles per hour and the weight of the dust particle as 6.5 x 10 ^{-10 }kg.

Note that expressing these numbers as, 67.1 x 10^{7 }or as, 0.671 x 10^{9 }and 0.65 x 10 ^{-11} or as, 6.5 x 10 ^{-10} are incorrect as per the norms of scientific notation although the values are same.

Below are the steps for rules of scientific notation

Here, we will see how to do scientific notation in computers and calculators:

Most of the computers and calculators do not have the provision to describe an exponent of 10 and hence, they use the letter E for the number 10 followed by another number that indicates the exponent. Thus a calculator will show,

6.71 x 10^{8 }as 6.71 E8 and 6.5 x 10 ^{-10 }as 6.5 E-10

Standard scientific notation places the decimal as first digit and drops the zeroes.

5.2300000000000

In the number 52,300,000,000,000 the coefficient will be 523

To find the exponent scientific notation calculate the number of places from the decimal to the last part of the number.

In 52,300,000,000,000 there are 11 places.

Therefore, we write 52,300,000,000,000 as: 523×10^{11}^{}

7.88 ×10^{5}

Step 1: First we see digit after the decimal point and put the decimal point after the first digit.

Step 2: Here the number 0.0035. When we put the decimal point we get 3.5.

Step 3: Count the number of places from decimal to last number and find the exponent form.

Step 4: Here the decimal points occur from left to right, so the power of 10^{th} must be minus.

Step 5: Hence the scientific notation in form of negative is 3.5 × 10^{-3}.

Answer: The scientific notation of 0.0035 is 3.5 × 10^{-3}.

Step 1: Put the decimal point after the first digit of the given number.

Step 2: Here the number 0.00504. When we put the decimal point we get 5.04.

Step 3: Count the number of places from decimal to last number and find the exponent form.

Step 4: Here the decimal points occur from left to right, so the power of 10th must be minus.

Step 5: Hence the scientific notation in form of negative is 5.04 × 10^{-3}.

Answer: The negative scientific notation of 0.00504 = 5.04 × 10^{-3}.

The decimal number 0.00000089 is written in scientific notation as 8.9 x 10^{-7}.

Since the decimal point was stimulated 7 places to the right to structure the number 6.5.

It is correspondent to 6.5 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1 x 0.1

Scientific notation numerals could be written in many different ways and so the numeral 6.5 x 10^{-7} might also be written as 6.5e-7.

To arrange your integer in this manner, we'll multiply 0.0000000023** **by 10, 9** **time(s), making it a 2.3.

Because, each multiplication by 10 move the decimal point to the right one digit.

But in arrange to remain our number the same numeral; we should have a × 10^{-9} next to the 2.3.

So, the final answer is 2.3 x 10^{-9}

0.0000000023 = **2.3 x 10**^{- 9}

To arrange our integer in this manner, we will multiply 0.0000000589** **by 10, 8** **time(s), making it a 5.89

because, each multiplication by 10 move the decimal point to the right one digit.

But in arrangement, to retain our number as the same numeral; we should multiply 10^{-8}** **with 5.89

So, the final answer is 5.89 x 10^{-8}

0.0000000589^{ }= **5.89 x 10**^{- 8}

** Step1: **Adjusting the exponents

Here** **12 x 10 ^{2 }having the smaller power. We can write 12 x 10 ^{2 }as 1.2 x 10 ^{3}

Now 1.2 x 10 ^{3 }and 5 x 10 ^{3 }having the same powers.

** Step 2:** Add the coefficient of the numbers.

Add 1.2 and 5

1.2 + 5 = 6.2

** Step 3:** Writing the result in scientific form

12 x 10 ^{2 }+ 5 x 10 ^{3 } = **6.2 x 10 ^{3 }**

** Step1:** Adjusting the exponents

Here** **0.3 x 10^{3}** **having the smaller power. We can write 0.3 × 10^{3} as 0.03 x 10 ^{4,} Now 0.03 x 10 ^{4 }and1.6 × 10^{4} ^{ }having the same powers.

** Step 2:** Adding 0.03 and 1.6

0.03+1.6 = 1.63

** Step 3:** Writing the result in scientific form

0.3 × 10^{3} + 1.6 × 10^{4 } =** 1.63 x 10 ^{4}**

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