Author Topic: Infinite Geometric sequence (Read 903 times) Tweet Share

Studyinghard · « **on:** June 24, 2010, 08:47:47 pm »

Find the fractional form
a) 0.1 recurring.
b) 0.09 (the little recurring dot over both 0 and 9)
c) 0.16 recurring.

TrueTears · « **Reply #1 on:** June 24, 2010, 08:59:21 pm »

http://vcenotes.com/forum/index.php/topic,25741.msg261332.html#msg261332

QuantumJG · « **Reply #2 on:** July 05, 2010, 08:49:16 pm »

Quote from: Studyinghard on June 24, 2010, 08:47:47 pm

Find the fractional form
a) 0.1 recurring.
b) 0.09 (the little recurring dot over both 0 and 9)
c) 0.16 recurring.

a)

0.1111111111..... = $\dfrac{1}{10} (1 + \dfrac{1}{10} + ( \dfrac{1}{10} )^{2} + ... )$

= $\dfrac{1}{10} * \dfrac{1}{1 - \dfrac{1}{10} }$

= $1/9$

b)

0.09090909.... = $\dfrac{9}{100} * ( 1 + \dfrac{1}{100} + ...)$

= $\dfrac{9}{100} * \dfrac{1}{1 - \dfrac{1}{100} }$

= $\dfrac{1}{11}$

c)

0.166666.... = $\dfrac{1}{10} + \dfrac{6}{100} * (1 + \dfrac{1}{10} + ... )$

= $\dfrac{1}{10} + \dfrac{6}{100} * \dfrac{1}{1 - \dfrac{1}{10} }$

= $\dfrac{3}{30} + \dfrac{2}{30}$

= $\dfrac{1}{6}$

QuantumJG · « **Reply #3 on:** July 05, 2010, 08:50:47 pm »

Just for fun.

Express 0.9999999999...... as a rational number.

moekamo · « **Reply #4 on:** July 05, 2010, 09:29:42 pm »

$0.\dot{9} = 1$

since $0.\dot{1} = \frac{1}{9}$ and multiplying both sides by 9 we have: $0.\dot{9} = \frac{9}{9} = 1$

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Author Topic: Infinite Geometric sequence (Read 903 times) Tweet Share

Studyinghard

Infinite Geometric sequence

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