Scientific Notation | Beginning Algebra - Lumen Learning

Learning Outcomes

• Define decimal and scientific notation
• Convert between scientific and decimal notation
• Multiply and divide numbers expressed in scientific notation
• Solve application problems involving scientific notation

Convert between scientific and decimal notation

Before we can convert between scientific and decimal notation, we need to know the difference between the two. Scientific notation is used by scientists, mathematicians, and engineers when they are working with very large or very small numbers. Using exponential notation, large and small numbers can be written in a way that is easier to read.

When a number is written in scientific notation, the exponent tells you if the term is a large or a small number. A positive exponent indicates a large number and a negative exponent indicates a small number that is between 0 and 1. It is difficult to understand just how big a billion or a trillion is. Here is a way to help you think about it.

1 billion can be written as 1,000,000,000 or represented as [latex]10^9[/latex]. How would 2 billion be represented? Since 2 billion is 2 times 1 billion, then 2 billion can be written as [latex]2\times10^9[/latex].

A light year is the number of miles light travels in one year, about 5,880,000,000,000.  That’s a lot of zeros, and it is easy to lose count when trying to figure out the place value of the number. Using scientific notation, the distance is [latex]5.88\times10^{12}[/latex] miles. The exponent of 12 tells us how many places to count to the left of the decimal. Another example of how scientific notation can make numbers easier to read is the diameter of a hydrogen atom, which is about 0.00000005 mm, and in scientific notation is [latex]5\times10^{-8}[/latex] mm. In this case the [latex]-8[/latex] tells us how many places to count to the right of the decimal.

Outlined in the box below are some important conventions of scientific notation format.

Scientific Notation

A positive number is written in scientific notation if it is written as [latex]a\times10^{n}[/latex] where the coefficient a is [latex]1\leq{a}