# 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 [10^{4}] shows how big the number is.

The exponent of the 10 is an integer.

## Example 1

### Example

### Solution

Find the front part and the decimal point.

The front part is the numbers next to the consecutive 0s.

For 310200, [3102] is next to the [00].

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 [3102] 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 (= 10^{1}).

So the exponent of 10 is plus: 5.

So the given number, 310200, is 3.102 × 10^{5}.

So 3.102 × 10^{5} is the answer.

## Example 2

### Example

### Solution

Find the front part and the decimal point.

The front part is the numbers next to the consecutive 0s.

For 0.00509, [509] 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 [509] 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 (= 10^{0}).

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.