fractions & decimal numbers

To calculate the decimal number that is equivalent to a fraction, we only have to divide:


To calculate the fraction that is equivalent to an exact decimal, we have to remove the decimal point and put in the denominator a unit with as many zeros after it as decimals the number has:

To calculate the fraction that is equivalent to a recurring decimal:

- If it is a pure periodic decimal:

- If it is an eventually periodic decimal, first we have to convert it into a pure periodic decimal:

NOTE: Then, only the recurring and the exact decimals are rational numbers.

Exercise.- 

1.- Calculate the decimal number that is equivalent to:

2.- Calculate the fraction that is equivalent to these decimal numbers:

a) 1.3838...

b) 22.2222222....

c) 17.35

d) 9.9999...

Solutions:

1.- a) 0.6363...; b) 0.8333...; c) 1.35; d) 0.9285714285714...

2.- a) 137/99; b) 200/9; c) 1735/100; d) 10