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

Like this:
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Or this:
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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?


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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.


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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?"

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When the number is 10 or greater, the decimal point has to move to the left, and also the power of 10 is positive.
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When the number is smaller than 1, the decimal allude has to relocate to the right, therefore the power of 10 is negative.


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 = 2.75×10-4

Then 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

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

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Values room rounded off, so 53,6870,912 is shown as simply 5×108

That 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 × 103
27,000 is composed 27 × 103270,000 is created 270 × 1032,700,000 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 ×10s 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