Sorry if it's a little hard to read.

Method for changing from repeating decimal to fraction in lowest terms.

1. Call the repeating decimal

*x*.

2. Multiply

*x*by a power of ten that has as many zeros as there are digits in the repeating part.

3. Subtract

*x*from the bigger number, which will cancel out the repeating part.

4*. IF the subtraction gives you a decimal number, multiply by some power of ten so you get (whole number times)

*x*= (some other whole number)

5. Divide both sides of the equation by the number multiplying

*x*.

6. Reduce the fraction to lowest terms.

Examples.

Example #1: .

1

*. x*= 0.16161616...

2. Because the repeating part has two digits, multiply

*x*by 100 to get 100

*x*= 16.16161616....

3. 100

*x*-

*x*= 16.1616161616... - 0.1616161616...

which reduces to 99

*x*= 16.

step 4 isn't needed.

5.

*x*= 16/99, which is reduced to lowest terms.

Example #2: .1

1

*. x*= 0.16666...

2. Because the repeating part has one digit, multiply

*x*by 10 to get 10

*x*= 1.6666....

3. 10

*x*-

*x*= 1.66666... - 0.166666...

which reduces to 9

*x*= 1.5

4. 1.5 isn't a whole number, so multiply by 10 on both sides to get 90

*x*= 15.

5.

*x*= 15/90, which is not in lowest terms.

6. 15/90 = 5/30 = 1/6.

Practice problems.

a) Find the fraction for .

b) Find the fraction for .2

c) Find the fraction for .2

Answers in the comments.

## 1 comment:

a)

x= .232323231.

x= 0.23232323...2. Because the repeating part has two digits, multiply

xby 100 to get 100x= 23.23232323....3. 100

x-x= 23.23232323... - 0.23232323...which reduces to 99

x= 23.step 4 isn't needed.

5.

, which is reduced to lowest terms.x= 23/99b)

x= .233333331.

x= 0.23333...2. Because the repeating part has one digit, multiply

xby 10 to get 10x= 2.3333....3. 10

x-x= 2.33333... - 0.23333...which reduces to 9

x= 2.1.4. Multiply by 10 to get 90

x= 215.

x= 21/90, which is not reduced to lowest terms.6.

.x= 7/30c)

x= .234343434...1.

x= 0.2343434...2. Because the repeating part has two digits, multiply

xby 100 to get 100x= 23.4343434....3. 100

x-x= 23.4343434... - 0.2343434...which reduces to 99

x= 23.2.4. Multiply by 10 to get 990

x= 2325.

x= 232/990, which is not reduced to lowest terms.6.

.x= 116/495Post a Comment