# Change Number to Scientific Notation

How to change a number to scientific notation: definition, 2 examples, and their solutions.

## Definition

### Definition

Scientific notation is a way to write a number
that is too big or too small.
There are two parts.

The front part [1.23] shows how the number looks like.
The front part is 1 ≤ [front part] < 10.
(The front part is called the [significand].)

The power part  shows how big the number is.
The exponent of the 10 is an integer.

## Example 1

### Solution

Find the front part and the decimal point.

The front part is the numbers next to the consecutive 0s.
For 310200,  is next to the .
So 3102 is the front part.

The decimal point is behind the end 0.
So draw the decimal point behind 310200.

Move the decimal point so that the front part  can be
1 ≤ [front part] < 10.
Then the front part is 3.102.
And the decimal point moved 5 digits.

The front part is 3.102.

The decimal point moved 5 digits.
So the exponent of 10 is either 5 or -5.

310200 is greater than 10 (= 101).
So the exponent of 10 is plus: 5.

So the given number, 310200, is 3.102 × 105.

So 3.102 × 105 is the answer.

## Example 2

### Solution

Find the front part and the decimal point.

The front part is the numbers next to the consecutive 0s.
For 0.00509,  is next to the [0.00].
So 509 is the front part.

The decimal point is already given: 0.00509.

Move the decimal point so that the front part  can be
1 ≤ [front part] < 10.
Then the front part is 5.09.
And the decimal point moved 3 digits.

The front part is 5.09.

The decimal point moved 3 digits.
So the exponent of 10 is either 3 or -3.

0.00509 is less than 1 (= 100).
So the exponent of 10 is minus: -3.

So the given number, 0.00509, is 5.09 × 10-3.

So 5.09 × 10-3 is the answer.