Lesson WHAT IS scientific notation

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Science often deals with numbers that are very large or very small.

For example, the Earth contains approximately 900000000000000000000000 atoms.

Such large numbers, written as I just did, are difficult to read and compare by humans. (They do not present any difficulties for a computer, however).

To make them more readable, people invented <I>scientific notation</I>. It is a way of writing down numbers.

<H4>Scientific notation form</H4>

Scientific notation is written as a decimal number between 1 and 10, followd by a power of 10.

Example:

1. {{{12800 = 1.28 * 10^4}}}

2. What is greater, 4800234000000 or 72229000000000? It is hard to say until you counted the digits. If you look at scientific notation of these numbers, you will see {{{4.800234*10^12}}} and {{{7.2229*10^13}}}. The second number is more that 10 TIMES the first one. So, it makes sense to use these numbers in books and computer printouts.

3. is 0.00000001 less than 1/1000000? It is easier to compare {{{1*10^(-8)}}} vs. {{{1/10^7}}}.

<H4>Multiplication and division of numbers in scientific notation</H4>

Multiplying and dividing numbers in scientific notation is an exercise from thye chapter on "powers of 10".

<B>Multiplying</B>:Multiply the small parts separately and the exponents separately, and write them together.

For example, {{{2.2*10^3 * 3*10^5 = (2.2*3) * (10^3*10^5) = 6.6 * 10^(3+5) = 6.6*10^8}}}.

<B>Dividing</B>:Multiply the small parts separately and the exponents separately, and write them together.

For example, {{{6*10^3 / (2*10^5) = (6/2) * (10^3/10^5) = 3 * 10^(3-5) = 3*10^-2}}}.