SCIENTIFIC NOTATION
Scientists use scientific notation to communicate very small or very large numbers.
Example:
3,600,000,000,000 or 3.6 trillion – who would want to write that number out for a calculation.
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We are interested in the 3 and the 6 for converting to scientific notation.
We need to move the decimal between the 3 and 6. To do this we must move twelve
spaces to the left!
This can be re-written as 3.6 x 1012
*Notice: the exponent is a positive number because we have a BIG number here.
Example:
0.0000067 is a really small number and all those zeroes can get awfully confusing! Let’s clean it
up a bit.
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Here, our interest is in the 6 and 7 – we want to move the decimal to be between the 6
and 7
This time, we need to move the decimal six spaces to the right!
This can be written as 6.7 x 10-6
Notice: the exponent is a negative number because we have a SMALL number here.
Now wait – how do we go the other way?!
Example:
8.65 x 10-8 – we can tell this is a really small number because of the negative exponent. Now
let’s take a look at how to convert it to a decimal.
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The negative 8 means we move the decimal eight places to the left!
Doing this, we end up with 0.0000000865
Example:
1.356 x 109 – we can tell this is a really big number because of the positive exponent.
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The positive 9 means we move the decimal nine places to the right!
Doing this, we end up with 1,356,000,000
If you are getting confused with which way to move the decimal – just remember a negative
exponent means small and a positive one means big… make sure you move it the right way to
get the right ‘size’ of number!
Your Turn!
a. 0.000056
b. 14,500,000,000
c. 6.78 x 10-5
d. 7.89 x 108
e. 850
f. 779.3 (convert to a number with 2 significant digits)
g. 4.5923 x 10-11 (convert to a number with 3 significant digits)