Standard Notation to Scientific Notation

Standard Notation to Scientific Notation

How to change standard notation numbers to scientific notation numbers: examples and their solutions.

Definition

a * 10^n. 1 ≤ a < 10, n: integer

Scientific notation is a way to express a number.

It's useful when the number is
very big or very small.

It consist of two parts:

a: how the number looks like (1 ≦ a < 10)
n: how big the number is

Example 1

Express the given number in scientific notation. 310200

310200 > 1.

So n (red) is (+).

Find the significant numbers (blue).
It's the part that starts
from the non-zero digit (3)
to the digit right before the 'end 0-s' appear (2):
3102.

Move the decimal point to make 1 ≦ (blue) < 10.
Then a = 3.102. (blue)

The decimal point moves 5 digits.
And n is (+).
So n = +5. (red)

So 310200 = 3.102 × 105.

Example 2

Express the given number in scientific notation. 0.00509

0.00509 < 1.

So n (red) is (-).

Find the significant numbers (blue).
It's the part that starts
from the non-zero digit (5)
to the digit right before the 'end 0-s' appear (9):
509.
(Behind 9, the 'end 0-s' are omitted: 0.0050900...)

Move the decimal point to make 1 ≦ (blue) < 10.
Then a = 5.09. (blue)

The decimal point moves 3 digits
And n is (-).
So n = -3. (red)

So 0.00509 = 5.09 × 10-3.