Question

Convert each of the following repeating decimals to a/b form, where a, b are integers and b ≠ 0.
#2a ¯
0.4
#2c ¯
1.396
#2e ¯
-2.34

Answer 1

2a.
0.4̅
=4/9

The numerator is obtained by moving the decimal point one place to the right.

The denominator is the number of "9" digits that correspond to the number of decimal places moved.

Answer 2

2c
2.34̅

First, consider only the decimal part as an integer, i=34.

Count the number of digits that repeat (x=1) and those that don't (y=1).

From i=34, strip of the part that repeats to get j=3

Subtract j from i to get the numerator=34-3=31.
The numerator is obtained by stringing together x 9's and y 0's, to get 90.
The fraction is then 31/90.

Add to the integral part (2) to get
2 31/90. Transform the number to the required form as required.

Answer 3

correction:
The <i>denominator</i> is obtained by...