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fractions and 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.

 

 

Exercises:

1.- Find the decimal numbers that are equivalent to these fractions:

a) 10/7

b) 5/8

c) 7/3

2.- Find the fractions that are equivalent to these decimal numbers:

a) 1.2345

b) 12.1121212...

c) 37.323232...

 

 

Solutions: 1.- a) 1.428571428571...; b) 0.625; c) 2.333...; 2.- a) 12345/10000; b) 11991/990; c) 3695/99