decimal to fraction

Question

Write the following expression as a fraction: 0.3545454 (with a line on the top of 54)

Answer 1

Let x = 0.3545454...

 

Since the repeating part has two digits, multiply by 10² = 100.

 

100x = 35.45454...

 

 

Subtract to rid of the repeating part: 100x - x = 35.1

 

35.1 is exact.

 

 

Solve for x:

 

99x = 35.1

 

x = 35.1/99 = 351/990 = 39/110

 

 

You can use this procedure to find fractional equivalents for your other problems.