# Scientific Notation

## What does it mean?

### Definitions:

Scientific Notation is the expression of a number n in the form $$a * 10^ b$$ where a is an integer such that $$1≤ |a| <10$$ and b is an integer too.

Multiplication: To multiply numbers in scientific notation, multiply the decimal numbers. Then add the exponents of the powers of 10. Place the new power of 10 with the decimal in scientific notation form. If your decimal number is greater than 10, count the number of times the decimal moves to the left, and add this number to the exponent.

Division: To divide numbers in scientific notation, first divide the decimal numbers. Then subtract the exponents of your power of 10. Place the new power of 10 with the decimal in scientific notation form. If the resulting decimal number is less than 1, move the decimal point to the right and decrease the exponent by the number of places that the decimal point moved.

## What does it look like?

### Express Large Numbers in Standard Form

$$n = 101325 = 1.01325 * 10^5$$ (Move the decimal point 5 places to the right)

### Express Small Numbers in Standard Form

$$n = 0.00092 = 9.2 * 10^ {-4}$$ (Move the decimal point 4 places to the left.)

### Multiplication:

$$(2.3 * 10^4) * (6.6 * 10^7)$$ First Step - $$2.3 * 6.6 = 15.18$$ Second Step - $$10^4 * 10^7 = 10^{11}$$ Because the new decimal number in step one is greater than 10, count the number of places the decimal moves to put the number between 1 and 10. Add this number to the exponent. In this case, the decimal point moves one place, so add 1 to the exponent. $$1.518 * 10^{12}$$

### Division:

$$(1.23 * 10^{10}) ÷ (2.4 * 10^2)$$ First Step - $$1.23 ÷ 2.4 = 0.5125$$ Second Step - (Subtract the exponents of the powers of 10) $$10^{10} ÷ 10^2 = 10^8$$ Because the decimal number is not between 1 and 10, move the decimal point one place to the right and decrease the exponent by 1. $$5.125 * 10^7$$

## You'll use it...

It’s used in a lot of places where very large or very small quantities need to be measured.

For example:

The numbers of atoms in a mole (chemistry).

The distances between the planets or stars in the universe, measured in miles.

And in the other extreme, for very tiny numbers, like the size or weight of an atom or molecule.

## Videos

### Scientific Notation Examples

Watch a Khan Academy Video »
Length: 12:49 Opens in player window

### Multiplying in Scientific Notation

Watch a Khan Academy Video »
Length: 7:35 Opens in player window