# 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

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