Many times in working science problems, you will have to raise a number in scientific notation to an exponential power. By far the most common power will be the second power, or squaring. So how do you square a number in scientific notation?
Remember that squaring involves taking a number times itself. For example,
42 = 4 X 4 = 16
b2 = b X b
So, if we square a number in scientifc notation, we take the number times itself, such as
(5 X 104)2 = (5 X 104) X (5 X 104)
Now we can take advantage of the fact that order does not matter in multiplication to regroup terms:
(5 X 104)2 = (5 X 104) X (5 X 104) = (5 X 5) X (104 X 104) = (25) X 108 = 2.5 X 109
Scientific notation really comes in handy when squaring large or small numbers. Squaring a large number only makes it larger, and squaring a small number only makes it smaller. Keeping track of all those zeroes can be difficult!
Try these by the "grouping" method above, and see if you see a pattern:
(3.45 X 1010)2
(4 X 10-5)2
(9.81 X 1021)2
Now check your answers, as well as your guess about the pattern.
Questions? Ask the designer, Jim Heath
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