Transcript Order-of-Magnitude

Order-of-Magnitude
By Jerry Kessler
What is Order-of-Magnitude?
• Order-of-Magnitude is a characteristic
associated with a value, distinguishing what
power of ten the number portrays - ie. Its
“magnitude”.
• In other words, Order-of-Magnitude describes
how large or how small the value is.
Example
• Example of numbers with the similar “Order-ofmagnitudes”:
– 32, 54, 24.9, 76, 92, 42, 12…
– 816, 459, 139, 846,…
– 6*105, 9.497*105, 4.2*105,…
• Notice how each group of numbers are within a
factor of 10 to each other
– ie. 12 & 92 are on the same order-of-magnitude
because they have the same “power of 10”…1.2*101
& 9.2*101.
Why is this Useful?
• It is useful to know to what “order-ofmagnitude” your result should be so that you
will have a good idea as to what the right
answer should look like.
• Estimation is useful in determining the
answer’s “order-of-magnitude” so that, when
you complete your rigorous calculations, you
can confer with your estimation.
Estimation Tip
• Therefore, be sure to only use estimations
that have the same “order-of-magnitude” as
the actual value.
• This way, you can be sure that your estimated
result will fall near the actual result.
The End