# Scientific Notation

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“Scientific Notation”, (also referred to as “Standard Form”), is used by Scientists to represent very large numbers, like the Distance between stars and planets, in a much simpler form.

It is also used by Geographers and Economists to represent very large numbers such as how many square kilometers in area a Country is, and how big in millions its population is, or how many billions of dollars its current debt level is at.

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Format of Scientific Notation

Scientific Notation always involves having a number that is between 1 and 10 multiplied by a Power of 10.

For example the distance from the earth to the sun is 149 600 000 km, and because this number is so big, it is usually listed in Scientific Notation.

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Helpful Tips for Dealing with Scientific Notation

Here are a couple of very useful tips to constantly keep in mind when doing any activities that involve Scientific Notation.

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

The following five minute video is an excellent explanation about why people use Scientific Notation.

Here is a quick video on how to convert Scientific Notation into a standard number value.

The following vidoe shows how to convert number values into Scientific Notation

Here is a quick video about how to write decimal values in Scientific Notation

Scientific Notation into Numbers

The following examples show how to convert Scientific Notation expressions into the actual numbers or decimals that they represent.

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Image Copyright 2013 by Passy’s World of Mathematics

Numbers into Scientific Notation

Converting Numbers into Scientific Notation is a little bit trickier than doing Scientific Notation into Numbers.

However we should be okay if:

We follow the set sequence of steps, (shown in the examples below) and

Remember our key facts from the “Helpful Tips”:

Normal Numbers bigger than 1, or large numbers, always have a POSITIVE Power of 10.

Values smaller than 1, usually decimal values, always have a NEGATIVE Power of 10.

The first part of Scientific Notation is always a number value that is between 1 and 10. (eg. 1, 1.5, 2.3, 3.167, 4, 5.21, 6.3, 8.20, 9.9999 etc)

The second part of Scientific Notation is a Power of 10 which tells us how many places the decimal point is moving.

Here are some examples showing the full working out steps.

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Because it can be easy to make little mistakes when converting into Scientific Notation, it is always an excellent idea to check our answers by working backwards and checking that our Scientific Notation does give us the back the original number or decimal that we started with.

It doesn’t take long to do this check, it is easy to do, and it guarantees us that we have the correct answer.

Here is how we can do a simple check for the example we just did above.

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Here is an example showing how to convert a Decimal Value into Scientific Notation.

REMEMBER that Decimal Values always produce Negative Powers of 10.

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The following example shows a very important exception rule for removing zeroes from Decimal values that we are converting into Scientific Notation.

ANY ZERO THAT CAME AFTER THE DECIMAL POINT IN THE ORIGINAL STARTING DECIMAL NUMBER MUST NOT BE REMOVED.

The reason why is a little complicated, but works like this.

If somebody wrote down a measurement as 0.0050, this means they measured it to four decimal places to the nearest ten thousandth, and it is 50/10000.

If they had only measured it to three decimal places to the nearest thousandth, then the value would have been recorded as 0.005 and it is 5/1000.

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If we have a Power of 10 like 10, 100, 1000, 10 000 etc, we can convert it into Scientific Notation as shown below.

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If we have a value which is between 1 and 10, then we can express it in Scientific Notation using the Power of Zero.

This is shown in the example below.

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Scientific Notation on Calculators

There are usually special buttons on calculators for entering values that are in Scientific Notation format into the calculator.

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