Scientific Notation
Scientific notation is a convention used
to express large numbers. A number written in scientific notation
has two parts:
-
A number between 1 and 10.
- The
power of 10 by which you must multiply the first number in order
to get the larger number that is being represented.
In the following examples, we’ll first write a number
and then express it in scientific notation:
Scientific notation is particularly useful
when a large number contains many zeroes or needs to be approximated
because of its unwieldy size. Approximating quantities in scientific
notation can prevent unnecessarily messy calculations. Look at the
following expression:
This is a pretty nasty product to find—even when you’re
using a calculator. By approximating each number using scientific
notation, we can make the problem a lot easier:
When we compare this approximation to the actual product,
we find that we were less than 1% off. Not too shabby.
Also, note the way in which we combined the terms in the
last example to make the multiplication a little simpler:
In general terms:
Often, this sort of simplification can make your calculations
easier.
Scientific Notation and Calculators
On many calculators, scientific notation is written differently
from what you’ve seen here. Instead of 3.1
10
33,
your calculator might read 3.1 E33. The capital letter “E” has the same
role as the “
10(power)”, only
it’s a little shorter. In general, scientific notation allows you
to work with numbers that might either be very tedious to manipulate
or too large to fit on your calculator.
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