Why Scientific Notation is used?

Scientists frequently work with numbers which are extremely large or extremely small. As an example, the distance of Sun from the Earth is 150 million kilometers. Thus, it’s difficult to write these kinds of numbers several times in our calculations. To overcome this problem, the scientist uses scientific notation to express these kinds of large numbers. It is a really practical tool for working with numbers which are either very large or very small.

Definition:

Scientific notation is defined as a standardized way to represent any quantity as the product of a real number and a power of 10.

How to Write?

a*10b

Here a is the real number which lies between 1 to 9 and b is the exponent of 10.

Example:

The number 550000 is written in the scientific notation as:

5.5*105

Here 5.5 is the real number which is between 1 and 10, while 5 is the exponent of base 10.

How to convert a number in scientific notation?

For large values:

  • We can explain this using the number 9850000000.
  • First of all, write the non-zero digits of a value.

985

  • Now put the decimal point after the first non-zero digit.

9.85

  • Count how many digits are after the first non-zero digit in the number. There are nine digits in our example.
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it shows that the exponent of 10 is 9.

  • Now we have a real number 9.85 which lies between 1 and 10, and the exponent of 10 which is 9. We can write the number in scientific notation as:

9.85*10^9

For small values:

  • We can explain this using the number 0.00000095
  • First of all, write the non-zero digits of a value.

95

  • Now put the decimal point after the first non-zero digit.

9.5

  • Now count the number of digits after the decimal of original value to the first non-zero digit (first non-zero digit is included)

We get 7. Now, -7 is the exponent of 10 in this value.

  • We can write the number in scientific notation as:

9.5*10^-7

Some Important rules while writing a number in scientific notation:
  • The base is always taken as 10.
  • Exponent will be non-zero integers both +ve or -ve.
  • The value of the real number must be between 1 and 10. it must not be less than 1 and greater than 10.
  • The real number may or may not have a -ve sign.
  • Itis compulsory to write all the significant figures after the decimal point.