Decimal expression of rational numbers

Calculate the decimal expression and the repeating of the following rational numbers:

  1. $\dfrac{7}{4}$
  2. $\dfrac{5}{11}$
  3. $\dfrac{5}{18}$

  1. If we do the division we obtain $\dfrac{7}{4}=1,75$, which is the decimal expression. There is no repeating.

  2. If we do the division we obtain $\dfrac{5}{11}=0,454545\ldots$

So the repeating is $45$ and the decimal expression is $0,\widehat{45}.$

  1. If we do the division we obtain $\dfrac{5}{18}=0,27777\ldots$

So the repeating is $7$ and the decimal expression is $0,2\widehat{7}$.

  1. The decimal expression is $\dfrac{7}{4}=1,75$. There is no repeating.
  2. The repeating is $45$ and the decimal expression is $0,\widehat{45}.$
  3. The repeating is $7$ and the decimal expression is $0,2\widehat{7}$

Calculate the expression as quotient of integers of the following rational numbers:

  1. $1,7\widehat{42}$
  2. $0,537\widehat{3}$
  3. $12,63\widehat{408}$

  1. According to our notation; $a=17, b=1.742, m=1$ and $n=2$. Then that corresponds to the quotient $$\dfrac{b-a}{990}=\dfrac{1.742-17}{990}=\dfrac{115}{66}$$

  2. According to our notation; $a=537, b=5.373, m=3$ and $n=1$. Then that corresponds to the quotient $$\dfrac{b-a}{9.000}=\dfrac{5.373-537}{9.000}=\dfrac{403}{750}$$

  3. According to our notation; $a=1.263, b=1.263.408, m=2$ and $n=3$. Then that corresponds to the quotient $$\dfrac{b-a}{99.900}=\dfrac{1.263.408-1.263}{99.900}=\dfrac{84.143}{6.660}$$

  1. $\dfrac{115}{66}$
  2. $\dfrac{403}{750}$
  3. $\dfrac{84.143}{6.660}$
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