Scientific Notation
4.1 Order of Operations
4.2 Numbers
4.3 Factors
4.4 Multiples
4.5 Fractions
4.6 Decimals
4.7 Percents
4.8 Exponents
4.9 Roots and Radicals
4.10 Scientific Notation
4.11 Logarithms
4.12 Review Questions
4.13 Explanations
Scientific Notation
Scientific notation is a convention used to express large numbers. A number written in scientific notation has two parts:
  1. A number between 1 and 10.
  2. 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 1033, 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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