**Scientific Notation **(also called Standard type in Britain) is a special means of creating numbers:

Like this: | ||

Or this: |

It renders it easy to use large and small values.

You are watching: Which number is written using standard scientific notation

## OK, exactly how Does the Work?

**In this example, 5326.6 is composed as 5.3266 × 103**,

**because 5326.6 = 5.3266 × 1000 = 5.3266 × 103**

## Try the Yourself

Enter a number and see it in clinical Notation:

Now shot to use clinical Notation yourself:

## Other ways of writing It

**3.1 × 10^8**

We have the right to use the **^** symbol (above the 6 top top a keyboard), as it is easy to type.

Calculators often use "E" or "e" choose this:

## How to do it

**To number out the power of 10, think "how countless places carry out I move the decimal point?"**

When the number is 10 or greater, the decimal point has to move to the left, and also the power of 10 is positive. | |

When the number is smaller than 1, the decimal allude has to relocate |

### Example: 3.2 is written 3.2 × 100

**We didn"t need to move the decimal point at all, for this reason the strength is 100**

But the is currently in clinical Notation

## Check!

After putting the number in scientific Notation, just inspect that:

The "digits" part is in between 1 and also 10 (it can be 1, however never 10)The "power" component shows precisely how many places to move the decimal point## Why use It?

Because it provides it much easier when taking care of very huge or very tiny numbers, which are common in Scientific and also Engineering work.

**Example: a tiny room inside a computer chip has actually been measured to it is in 0.00000256m wide, 0.00000014m long and 0.000275m high. **

**What is that volume?**

Let"s very first convert the 3 lengths into scientific notation:

width:0.000 002 56m = 2.56×10-6length: 0.000 000 14m = 1.4×10-7height: 0.000 275m = 2.75×10-4Then main point the digits with each other (ignoring the ×10s):

2.56 × 1.4 × 2.75 = 9.856

Last, multiply the ×10s:

10-6 × 10-7 × 10-4 = 10-17 (easier 보다 it looks, simply **add −6, −4 and −7** together)

The an outcome is **9.856×10-17 m3**

It is supplied a lot in Science:

### Example: Suns, Moons and also Planets

The Sun has actually a massive of 1.988 × 1030 kg.

Easier than creating 1,988,000,000,000,000,000,000,000,000,000 kg**(and the number provides a false sense of numerous digits the accuracy.)**

## Play v It!Use scientific Notationin gravity Freeplay |

It can likewise save space! right here is what happens when you double on each square the a chess board:

Values room rounded off, so 53,6870,912 is shown as simply 5×108That critical value, shown as 9×1018 is actually 9,223,372,036,854,775,808

## Engineering Notation

Engineering Notation is favor Scientific Notation, except that we only use strength of ten that room multiples the 3 (such as 103, 10-3, 1012 etc).

See more: What Are The Possible Consequences Of Adding An Organism To A Food Chain?

### Examples:

2,700 is written 2.7 × 10327,000 is composed**27 × 103**270,000 is created

**270 × 103**2,700,000 is written

**2.7 × 106**

### Example: 0.00012 is written **120 × 10-6**

Notice that the "digits" part can currently be between 1 and 1,000 (it have the right to be 1, yet never 1,000).

The benefit is the we have the right to replace the **×10**s through Metric Numbers. Therefore we have the right to use standard words (such as thousand or million), prefixes (such together kilo, mega) or the prize (k, M, etc)

Example: 19,300 meter is created **19.3 × 103 m, or 19.3 km**

Example: 0.00012 seconds is created **120 × 10-6 s, or 120 microseconds**

powers of 10 decimals Metric numbers Lengths from Very tiny to Very big Exponents