Scientific notation is used to write much larger or smaller numbers as a decimal number between 1 and 10, multiplied by 10 to some power. This allows for representation of small or large numbers in a compact form, and can ease order of magnitude estimations.

### Learning Objectives

**Summary:** Students will be expected to perform conversions to scientific notation, mathematical operations using scientific notation, and use commutativity and scientific notation to mentally perform order of magnitude calculations.

Students will be able to…

- Convert a number into scientific notation.
- Perform mathematical operations using scientific notation.
- Use the commutative property of algebra and scientific notation to perform basic calculations to an order of magnitude in their head.

## BoxSand's Resources

### Text

Example: Speed of light in a vacuum $c = 299,792,458 m/s$ (not scientific notation), or approximately $3.00*10^8 m/s$ (scientific notation). Use the commutative property of multiplication to carry out calculations in scientific notation, for example:

Find the distance light travels in 1.2 pico seconds.

$c$ is the speed of light in a vacuum, and let $\Delta t$ represent the change in time. |$\Delta \overrightarrow{r}$| will represent the distance travelled, which you will see more of in Kinematics. Start out by representing the situation symbolically:

$$|\Delta \overrightarrow{r}| = |\vec{v}|\Delta t = (3.00*10^8 m/s)(1.2*10^{-12}s)$$

Now use the commutative property to switch the exponents:

$$= 3.00*1.2*10^8*10^{-12}m$$

$$=3.6*10^{-4}m$$.

### Video

Scientific Notation (6 min)

## Web Resources

### Text

Scientific Notation, Metric Prefixes, and Conversions -- **Physics Lab**

### Video

**Veritasium** video on scientific notation

https://www.youtube.com/watch?v=WwmJ5nMmigQ

Walter Lewin lecture covering much of the material to be reviewed

### Simulation

Let us know if you have a suggestion simulations!

## Practice

### Practice Problems

Here's some practice converting numbers into scientific notation from Kuta Software: Scientific Notation Practice.

## Problem Solving Help

### Tips and Tricks

When converting numbers to scientific notation, remember that the leading coefficient should always be less than 10. Also, it is useful to count the number of digits to the right or left of the decimal place. If you count 10 digits to the left, there will be a __positive__ 10 in the exponential. If you count 10 to the right, there will be a __negative__ 10 in the exponential.