Introduction: Today, we are going to be converting numbers like 0.22222222…. into fractions. At the end of this lesson will come up with a surprising result: 1 = .99999…..

This is not a trick…IT IS THE TRUTH. To prove this, it will require a minimum amount of effort. Let’s start by learning how to convert decimals into fractions.

Converting Decimals to Fractions Part 1:

To convert a decimal that stops after awhile, it is easy.

Example: Convert 0.235 into a fraction

Solution: Notice that our decimal stops at the thousandths place, so we just put our number over a 1000:

Example: Convert 0.15 into a fraction _______________

Converting Decimals to Fractions Part 2:

Life gets a little harder when our decimal goes on forever. Before we start, we are going to introduce some notation to make our lives easier. Instead of writing decimals like 0.1232323232323…., we make our lives less confusing by writing this as follows: 0.1232323… =

Example 1: Convert 0.222222…. into a fraction.

Solution: Instead of writing 0.22222…., we write

Let x = =0.222……

Then 10x = 2.2222222… ( = )

                 - x = 0.222…….

                9x = 2

Solution: Again, let x = .

What do we need to multiply by to solve this problem? _____________

Solution: Again, let x =

What do we need to multiply by to solve this problem? ____________

On your own now, convert the following decimals into fractions.

DON’T FORGET TO REDUCE when possible.

a.) 0.345                                               a.)_____________

 

 

 

b.) 0.1477                                             b.)_____________

 

 

 

c.)                                                  c.)_____________

 

 

 

d.)                                          d.)_____________

 

 

 

e.)                                                      e.)_____________

 

 

 

f.)                                                      f.)_____________

 

 

 

g.)                                                  g.)_____________