Property 8
Repeating Periodical Decimals
Every rational number either as a terminating or as a repeating periodically decimal is written in the form of a decimal number and the repeated decimals by the drawing a line segment over the digits which are repeated.
\(0{,}\overline x=0{,}xxx\ldots\)
\(x{,}y\overline{zt}=x{,}yztztzt\ldots\)
Changing of Repeating Periodical Decimal Number to Rational Number
\(\samefrac{\text{The whole of the number - Non-repeating part}}{\begin{gathered}\text{After the decimal point as many nines as the number of repeating}\\\text{digits and as many zeros as the number of non-repeating digits are}\\\text{written.}\end{gathered}}\)
\(ab{,}c\overline{de}=\samefrac{abcde-abc}{990}\)
\(=ab+\samefrac{cde-c}{990}\)
Repeating Periodical Decimals
If the repeating numer is only 9 at repeating decimal number, the first number at the left of 9 is increased 1 in numerical value and 9 is erased.
\(0{,}\overline9=1\)
\(3{,}4\overline9=3{,}5\)
1.
\(\samefrac{1}{3}=?\)
2.
\(0{,}44444\ldots=?\)
3.
\(3{,}\overline7=?\)
4.
\(0{,}\overline{15}=?\)
5.
\(1{,}0\overline2=?\)
6.
\(2{,}\overline{15}=?\)
7.
\(0{,}\overline{372}=?\)
8.
\(3{,}0\overline{42}=?\)
9.
\(12{,}3\overline5=?\)
10.
\(0{,}12\overline{13}=?\)
11.
\(2{,}\overline{612}=?\)