express-the-number-3-13-as-a-decimal-ane-state-the-value-of-the-300-th-value-

Question Number 135609 by physicstutes last updated on 14/Mar/21

express the number \frac{3}{13} as a decimal ane state the

value of the 300^{th} value

Answered by Olaf last updated on 14/Mar/21

\frac{3}{13} = 0, \overset{―}{230769}

we verify that 230769 \underset{n = 1}{\sum^{\infty}} 10^{- 6 n}

= 230769 \times 10^{- 6} \frac{1}{1 - 10^{- 6}} = \frac{230769}{10^{6} - 1}

= \frac{230769}{999999} = \frac{3 \times 76923}{13 \times 76923} = \frac{3}{13}

300 = 6 \times 50

the 300 th decimal is the same than

the 6 th decimal : 9

Commented by physicstutes last updated on 14/Mar/21

thanks a lot sir