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: .[16]

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[6] = 0.166666....

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 .[35]

b) Find the fraction for .3[5]

c) Find the fraction for .3[54]

Answers in the comments.

**Click on this link for more practice problems with solutions.**

## 1 comment:

a) Find the fraction for .[35]

1.

x= 0.35353535...2. Because the repeating part has two digits, we multiply

xby 100 to get 100x= 35.353535...3. 100

x-x= 35.353535... - 0.353535...which reduces to 99

x= 35.Step 4 isn't needed because we have no decimals.

5.

, which is reduced to lowest terms.x= 35/99==

b) Find the fraction for .3[5]

1.

x= 0.35555...2. Because the repeating part has one digit, we multiply

xby 10 to get 10x= 3.55555...3. 10

x-x= 3.55555... - 0.355555...which reduces to 9

x= 3.2.4. Because 3.2 is a decimal, we multiply both sides of the equation by 10 to get 90

x= 32.5.

x= 32/90, which is not reduced to lowest terms.6.

x= 16/45.==

c) Find the fraction for .3[54]

1.

x= 0.3545454...2. Because the repeating part has two digits, we multiply

xby 100 to get 10x= 35.45454543. 100

x-x= 35.4545454... - 0.3545454...which reduces to 99

x= 35.1.4. Because 35.1 is a decimal, we multiply both sides of the equation by 10 to get 990

x= 351.5.

x= 351/990, which is not reduced to lowest terms because both numbers are divisible by 3.6.

The last answer is lowest terms.x= 117/330 = 39/110.Post a Comment