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# An Introduction to Scientific Notation. - Algebra Class

Scientific notation can also be used for very small numbers in much the same way. 0.000005 is written as 510-6, because you use negative exponents on the 10 when the number is very small. Instead, the number could be written as. Then you can change the to an easier to understand number: 1012. Putting it all together, we have 6 1012. Now you can compare that number to others, because the 1012 means there are 12 zeroes at the end. Scientific notation is, essentially, a method for writing really big or really small numbers. It is called scientific notation because these huge numbers are often found in scientific work, like the size of an atom or the mass of the earth. Instead, scientific notation allows us to multiply 5 107 times 3 106. You multiply the 5 and the 3 to get 15, and then add the exponents on the 10s. The answer is 151013.

However, in order for scientific notation to be completely correct, the number at the beginning must be between 1 and 10. The 15 has to be changed into 1.5, and to make up for this we multiply the whole thing by another factor of 10, giving 1.51014. For example, you might have the number. Thats really big, right? Unfortunately, it isnt easy to tell exactly how big at first glance with all those zeroes stuck on the end. The value of scientific notation becomes clear when you try to multiply or divide these numbers. What is? You could do this relatively easily by multiplying 3 times 5 and then adding up all the zeroes, but that still takes time, and you could easily miscount all the zeroes.

Here are a few more examples to illustrate the principles of scientific notation:.8 710-3.007 (5108 41015) 2 1024 (510-8 41015) 2 108 (9106) / (3104) 3102 (when dividing, you subtract the exponents) (810-5) / (210-3) 410-2.
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