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.- Calculate the equivalent fractions to these decimal numbers:
a) 21.34
b) 1.333333...
c) 21.0212121...
d) 1.83333...

2.- Convert into fractions and calculate:
a) 1.333...+ 0.2 + 0.0666... =
b) 0.25 + 0,142857142857.... =

Solutions: 1.- a) 2134/100; b) 4/3; c) 20811/990; d) 33/18
2.- a) 8/5; b) 11/28

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