# From decimal numbers to fractions

## From exact numbers to fractions

In the numerator we write down the whole number without a comma and in the denominator we write down the number $$1$$ with as many zeros as digits has the decimal part.

Express the number $$1,8182$$ as a fraction. In the numerator we put the number without comma and in the denominator we write $$1$$ continued by $$4$$ zeros, because the decimal part has $$4$$ digits: $$\dfrac{18182}{10000}=\dfrac{9091}{5000}$$

Express the number $$4,51$$ as a fraction. $$\dfrac{451}{100}$$

## From periodic numbers to fractions

if it is a pure periodical decimal, in the numerator we write down the whole number without a comma by subtracting its integer part. In the denominator we write down as many nines as digits has the period.

Express the number $$1,\widehat{3}$$ as a fraction: $$\dfrac{(13-1)}{9}=\dfrac{12}{9}=\dfrac{4}{3}$$

Express as a fraction the number $$19,\widehat{62}=\dfrac{(1962-19)}{99}=\dfrac{1943}{99}$$

The conversion from ultimately periodic decimal to fractions is done in a similar way. The idea is to turn the decimal into a pure periodic by multiplying it by the appropriate potency of $$10$$.

$$13,85\widehat{32}=\dfrac{1385,\widehat{32}}{100}=\dfrac{1}{100}\dfrac{138532-1385}{99}$$

$$13,85\widehat{32}=\dfrac{137147}{9900}$$