+0

# 0.346 recurring = ?/99

0
176
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im doing real number and scientific/decimal notation stuff. How can i simplify 0.346 recurring as a fraction out of 99?

Guest Feb 16, 2017

#2
+19495
+10

0.346 recurring as a fraction?

$$\begin{array}{|rcll|} \hline 1000\cdot 0.\overline{346} &=& 346.\overline{346} \\ 1\cdot 0.\overline{346} &=& 0.\overline{346} \\\\ 1000\cdot 0.\overline{346} - 1\cdot 0.\overline{346} &=& 346.\overline{346}-0.\overline{346} \\ 999\cdot 0.\overline{346} &=& 346 \\ 0.\overline{346} &=& \frac{346}{999} \\ \mathbf{ 0.346\ recurring } &\mathbf{=}& \mathbf{ \frac{346}{999} }\\ \hline \end{array}$$

heureka  Feb 16, 2017
#1
0

.346346346.......=346/999.

Guest Feb 16, 2017
#2
+19495
+10

0.346 recurring as a fraction?

$$\begin{array}{|rcll|} \hline 1000\cdot 0.\overline{346} &=& 346.\overline{346} \\ 1\cdot 0.\overline{346} &=& 0.\overline{346} \\\\ 1000\cdot 0.\overline{346} - 1\cdot 0.\overline{346} &=& 346.\overline{346}-0.\overline{346} \\ 999\cdot 0.\overline{346} &=& 346 \\ 0.\overline{346} &=& \frac{346}{999} \\ \mathbf{ 0.346\ recurring } &\mathbf{=}& \mathbf{ \frac{346}{999} }\\ \hline \end{array}$$

heureka  Feb 16, 2017