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Scientific Notation

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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What is 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.

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 108

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


Scientific Notation Definition

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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 10n, 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 108 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 107 or as, 0.671 x 109 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.


Scientific Notation Rules

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Below are the steps for rules of scientific notation
Step 1: The coefficient should be bigger than or equivalent to 1 and less than ten,
Step 2: The base should be ten
Step 3: The exponent must explain the number of decimal place that the decimal need to be moved to modify the number to standard notation.
Step 4: A negative exponent means so as to the decimal is moved to the left when varying to standard notation.

How to do Scientific Notation

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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 108 as 6.71 E8 and 6.5 x 10 -10 as 6.5 E-10

Standard Scientific Notation

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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: 523×1011
Example: 78800000

7.88 ×105

Negative Scientific Notation

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In this negative scientific notation, a number in the standard form would be written in the form of a × 10-b, where a is the number lies in between 1 to 10 and b is the amount of times you multiply a.

Solved Examples

Question 1: Let see how to write this number 0.0035 in negative scientific notation.
Solution:
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 10th 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.


Question 2: Write the standard form of the number 0.00504
Solution:
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.


Decimal Scientific Notation

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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.

Solved Examples

Question 1: Decimal to scientific notation 0.0000000023
Solution:

To arrange your integer in this manner, we'll multiply 0.0000000023 by 109 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



Question 2: Decimal to scientific notation 0.0000000589
Solution:

To arrange our integer in this manner, we will multiply 0.0000000589 by 108 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



Scientific Notation Examples

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Below are some examples of scientific notation

Solved Examples

Question 1: Add the numbers 12 x 10 2 and 5 x 10 3 and give your result in scientific notation.
Solution:
 

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 103


 

Question 2: Add scientific notations 0.3 × 103 and 1.6 × 104
Solution:
 

Step1: Adjusting the exponents

Here 0.3 x 103 having the smaller power. We can write 0.3 × 103 as 0.03 x 10 4, Now 0.03 x 10 4 and1.6 × 104 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 × 103 + 1.6 × 104 = 1.63 x 10 4


 

Scientific Notation Practice

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Below you could see scientific notation problems

Practice Problems

Question 1: What is the scientific notation for the number 452354?
Question 2: What is the scientific notation for the number 0.007989?
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Convert to Scientific Notation Adding and Subtracting Scientific Notation
Multiplying Scientific Notation Dividing Scientific Notation
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